9/13/2023 0 Comments Image jpg converter![]() ![]() Simply double-clicking the JPG file will usually result in its opening in your default image viewer, image editor, or web browser. If you need even better compression, you can convert JPG to WebP, which is a newer and more compressible file format.Īlmost all image-viewer programs and applications recognize and can open JPG files. You can use our compress JPEG tool to reduce the file size by up to 80%! As such, the relatively small size of JPG files makes them excellent for transporting over the Internet and using on websites. The considerable compression that JPG offers is the reason for its wide use. JPG (Joint Photographic Experts Group), is a universal file format that utilizes an algorithm to compress photographs and graphics. For a multi-platform viewer, try XnView MP.ĭeveloped by: International Organization for Standardization (ISO) To open RAW on Microsoft Windows or macOS, use the options described above. After post-processing (editing) RAW files are usually converted to a JPEG ( RAW to JPG), PNG, TIFF, or BMP file type. For example, Canon (CR2), Nikon (NEF), Sony (SR2), Epson (ERF), Kodak (KDC), Panasonic (RW2), and others.Īlternatively, you may use a universal image viewer, such as Adobe Photoshop, Adobe Lightroom, or Zoner Photo Studio (an alternative to Adobe products). Determining the manufacturer is easy because they assign their own extension to RAW files taken using one of their cameras. The best way to open a RAW file is to use the software the camera manufacturer developed specifically for that purpose. Both open-source and proprietary RAW file types currently exist. Information can include the conditions that were present when the picture was taken, as well as descriptive text. A RAW file is an unprocessed image with all of its original information intact, as captured by the camera’s sensor. Unlike other file formats and extensions, the term RAW is not an acronym or an initialization.
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9/13/2023 0 Comments Top crossover 2021The Porsche Cayenne has a base MSRP of $68,850 and is a great mixture of Porsche's sporty past and roomy SUV design of the present. Similar to other sports car automotive brands, Porsche has stepped into the SUV manufacturing market offering a unique driving experience. Porsche is a well-known brand in the sports car market. The Lexus RX 350 has one of the lowest base model pricing in the midsize luxury SUV market, and ,with the options available upon purchase, the RX 350 is a bargain for what you pay for it.īrowse Lexus RX 350 listings here. The 2021 RX 350 has a base MSRP of $54,155 for the FWD model, with the top trim all-wheel-drive model starting at $56,840. The RX 350 is luxurious on the inside with plenty of cargo area and leg room for all passengers. Built with industry-standard safety features such as blind-spot monitoring, rear cross-traffic alert, and power-folding/auto-dimming outside mirrors. Lexus is known for its dependability and longevity. Both offerings seat 5-7 passengers and boast a 290hp engine offering 20 mpg city and 27 mpg highway. ![]() The Lexus RX 350 is offered in two drivetrain configurations, either a front-wheel-drive option or an all-wheel-drive option. Offered in both a two-door or four-door body design, the Defender seats up to six individuals or seven individuals based on the three-row SUV or two-row body style.īrowse Land Rover Defender listings here. The Defender comes with three different engine options, either a 296-hp 2.0-liter turbo-four, a 395-hp turbocharged inline-six, or a 518-hp supercharged V-8.ĭepending on your engine choice, the Defender has a very low MPG rating, and does not offer quite the interior you come to expect of a luxury SUV in 2021. The towing capacity of the Defender is 7,716 - 8,201lbs. With a base MSRP of $49,000 and a top-end price of $100,000, the Defender is by far the most capable SUV in its class. The 2021 Land Rover Defender is equipped with an all-wheel-drive powertrain with locking differentials allowing for intense off-roading experiences. Off-road ruggedness is not exactly your first thought when looking to purchase a midsize luxury SUV but practicality is. The GLE is also equipped with an easy-to-use infotainment system compatible with both Apple Carplay and Android Auto.īrowse Mercedes-Benz GLE Class listings here. The interior of the GLE is where the SUV truly shines as a luxury car, providing an ample amount of space for all passengers, and inclusive of a third-row option. Base MSRP for the GLE starts at $55,800 and quickly climbs from there depending on your choice of engine and trim level ending with the popular AMG trim level. New for 2021, the GLE is offered in both SUV and a coupe variant which offers a unique styling option for those who do not want the standard SUV look. The GLE is offered in three differing engine opinions, which correspond with the offered trim levels.Įngine options start with a 255-hp turbocharged 2.0-liter inline-four mid-range 362-hp turbocharged 3.0-liter inline-six, and the most powerful option of a 483-hp twin-turbocharged 4.0-liter V-8 with 21-hp AC electric motor producing an astounding 504 combined horsepower which is impressive for a compact SUV. The GLE-class offered by Mercedes-Benz is the company's mid-level entry to the Mercedes-Benz lineup of compact SUVs. The X5 is offered in both RWD or AWD powertrains.īrowse BMW X5 listings here. With an ample amount of space, the X5 offers seating for five or an added third row seat bumps seating up to seven. Starting at an MSRP of $60,395, the X5 is offered with your choice of a 335-hp turbocharged 3.0-liter inline-six 282-hp turbocharged 3.0-liter inline-six with an 112-hp AC electric motor with a 389 combined horsepower or a monster 523-hp twin-turbocharged 4.4-liter V-8 motor.īeing a midsize luxury SUV, BMW offers a multitude of optional interior features such as massaging seats, heated armrests, and a Bowers & Wilkins surround-sound system. ![]() The X5 series by BMW is known for its accumulation of sport, comfort, and technology, which is exactly what to look for in a midsize luxury SUV. New for 2021, BMW now offers the BMW X5 in a plug-in hybrid model known as the xDrive45e. With offerings from big-name automotive brands like BMW, Mercedes-Benz, Porsche, and Range Rover, how do they all stack up against each other and what makes each unique?įrom the rugged dependability of the Land Rover Defender to the first-in-class luxury of the Mercedes-Benz GLE, here are the 15 best luxury SUVs and Crossover SUVS for 2021. There are not many automotive markets as competitive as the midsize luxury SUV market. 9/13/2023 0 Comments Garfield kart twitterDo not miss these sweet position points,Įspecially since in the event of a tie, the grade will be used to settle it. RUMP Pinned Tweet Garfield Kart Garfieldkart -4h MAKE AMERICA GREAT AGAW Being a. Use crazy bonus objects such as the Pillow. GARFIELD KART FURIOUS RACING COMPARISON WITH THE ORIGINAL GARFIELD KART. Make a quick getaway off the starting line first and control skids to outrun your opponents. It's the ratio of the total number of points you've accumulated and the number of races started. Garfield Kart - Furious Racing is a 'Very Positive' Steam rated cult classic racer that lets you choose your character and kart according to their characteristics and your driving style. Your grade indicates your performance as a driver. Finally, there are 12 Grades from C- to S+ From baking cakes to racing in Garfield Kart, the two have amazing chemistry that could be a solid catch for 100T. Garfield, the famous lasagna-loving cat is back to take on Jon, Odie and company in a no-holds-barred racing gameChoose your character and kart according.PROTIP: Press the and keys to navigate the gallery, 'g' to view the gallery, or 'r' to view a random. So in total you won : 3 + 8 + 16 + 6 + 12 = 45 points! Twitter - GARFIELD KART Like us on Facebook Pin Tweet. For the Grand Prix, you will earn the points for each race + points for your final position in the cup.įinal Result of the cup : 2nd place > +12 points.You will then earn points by completing races player NA DBD Artist Main Socials twitter Follow Goal: 746/1000. you choose Take part in no-holds-barred crazy races. Catch up on the latest and greatest Garfield Kart: Furious Racing videos on. Utiliza tus mejores técnicas de conducción y los objetos bonus para cruzar la línea de meta en primera posición, pero ten cuidado. First of all, players will need to complete 10 races that will define your worldwide rank Join Garfield and his friends in the funniest fast and fur-ious game What character do you want to play with Garfield, Odie, Jon, Nermal.While most changes have been reverted or redesigned here, elements like the Mario jingle are still present. ![]() This hack is based on the 2008 NES hack “Mario Kart” by Elbobelo and the 2017 version by PacnSacDave. /pol/ pays tribute to based GarfieldKart twitter account : r/4chan 3K votes, 127 comments. Hop in and enjoy the ultimate in video racing competition on your NES. Start with Garfield and unlock Jon Arbuckle and Odie. But when the going gets rough, you’ll use bombs and missiles to knock the competition for a loop and make sure you’re the winner! Collect the letters that spell GARFIELD and upgrade to a faster, more powerful kart. Play garfield kart today on all platforms (or say goodbye to your family) chernobyl Joined March 2022. It’s you against four other all star-racers in this thrilling Nintendo kart racing competition! You’ll face hair pin turns, outrageous curves, oil slicks and rain clouds as you make your way through 32 treacherous courses that will test your driving ability like never before.Īlong the way, you’ll pick up performance boosters like Turbo Acceleration, Sticky Tires, and Top Speed that will help you get to the finish line first. User Ratings: 13 Our Review: Scroll Down Add to Games Collection Overview Reviews News Screenshots Discussions Reviews Nintendo Switch Garfield Kart Garfield Kart Furious Racing Review. Grab your controller and pull up to the starting line. Join America’s favorite cartoon cat Garfield, Odie and Jon Arbuckle. 9/13/2023 0 Comments Licecap on wine![]() But with today's broadband speeds, GIFs have become perfectly viable.Īlthough you might still want to use Photoshop to convert real videos into good GIFs. ![]() Sure, it sucks that video on the web and in presentation is still not a very well solved problem and takes more fumbling around than necessary. No worrying about sound or converting the recorded video into GIF form. No fumbling around with selecting regions and hidden control windows. The app will automatically save an animated GIF file when you're done recording. You open the app, put it over the content you want to record, click a button and away you go. My favourite part of using LICEcap is that it's simple. It also came in handy for the talk I gave about d3.js a few weeks ago where I wanted to show people animated graphs, but didn't want to keep jumping in and out of the presentation and fumbling around with a thousand windows. If you want to simply embed some moving parts into your blogpost - GIF.įor example, I used LICEcap to make those gifs of Super Mario playing with himself for Week 2 of the 52papers challenge. It won't help you create the next Railscasts or Coursera, but if you want to make something move in your slides when giving a talk, you need a GIF. The best example of doing one thing and doing it well. Kudos to everyone who makes educational screencasts to help people learn programming.īut LICEcap really is the best screen recorder I've ever used. Typing under pressure from a screen recorder is really hard. LICEcap - best screen capture tool I've ever used 9/12/2023 0 Comments Quarter dollar coins worth money![]() Sculptor-engraver William Cousins modified the Washington bust design in 1999 to help make more space on the coin for the various designs in the 50 State Quarter series. John Flanagan designed the portrait of George Washington depicted on the obverse (heads side) of the Washington quarter beginning in 1932.Here are a few cool facts about the 1999 Connecticut quarter and the New England state it honors: There’s so much interesting trivia about the quarters that pay homage to “The Constitution State.” But if you find a super-nice one, or one with an error, you may have hit the jackpot! Fun Facts About Connecticut And Its State Quarter So… 1999 Connecticut state quarters aren’t rare coins. Here’s how many Connecticut state quarters were made: Here are 3 of the most popular types of Connecticut quarter errors you should be looking for: No worries!… There are many other kinds of errors to look for on your Connecticut state quarters. Have you had a hard time finding any 1999 Connecticut state quarters struck on wrong-metal planchets? Other Types Of Connecticut Quarter Errors You can take your coin to a reputable coin dealer or have it certified by a third-party coin-grading company. If any of your 1999 Connecticut state quarters seem to match the characteristics listed above, then it’s worth having it checked out by a numismatic professional. Edge - The 1999 Connecticut quarter error doesn’t contain any edge reeding (those vertical lines on the edge of a normal quarter) - this quarter has a smooth edge.Color - The Connecticut error coin will appear gold, or even greenish in color.Thickness - Does your quarter look thicker than normal? A 1999 error quarter does.Weight - This Connecticut error quarter registers between 5.9 and 6.3 grams in weight - much heavier than the normal 5.67-gram weight for a regular copper-nickel clad Connecticut state quarter.So… how can you tell if you’ve got a rare Connecticut quarter error struck on a Sacagawea dollar planchet or an ordinary quarter with gold toning? Here are a few things you can check to see if you’ve got the rare Connecticut quarter error: These are super rare and super valuable experimental planchet errors! These “ experimental quarters” are quite rare - only a few were made representing each state (Delaware, Pennsylvania, New Jersey, Georgia, Connecticut) from the first year of the 50 State Quarters series. There’s one type of Connecticut quarter error worth as much as $10,000!Īpparently, a few of the 50 State Quarters from 1999 were struck on the planchets (coin blanks) designed for the Sacagawea dollar. Other fun facts about the Connecticut state quarter What’s The Most Valuable 1999 Connecticut Quarter Error?.How many Connecticut quarters were made.Which 1999 Connecticut error quarters you should be looking for. ![]() The most valuable Connecticut state quarter.So… which Connecticut quarters are worth the big bucks? And which ones are worth just 25 cents? Some 1999 State Quarters are even worth hundreds or thousands of dollars - no joke! Have you found a Connecticut quarter and want to know what it’s worth?īelieve it or not, many 1999 Connecticut state quarters are worth far more than their 25-cent face value. 9/12/2023 0 Comments Non alcoholic beer californiaIt has just enough citrus and hoppy bitterness to satisfy IPA fans, but it’s not overwhelming on the palate for drinkers who prefer a less assertive beer. We found Brooklyn Brewery’s Special Effects to be the most impressive. Whether you prefer a light, refreshing beer or a rich, thick stout, there are flavorful brews available to satisfy almost any beer drinker looking for a nonalcoholic option. “But nonalcoholic beer is expected to grow by double digits in the next few years with recent trends in health and wellness.” Beer giant AB InBev, which owns Golden Road, has even set a goal for at least 20 percent of its global beer volume to be no- or low-alcohol by 2025. “The current nonalcoholic space is 1 percent of the U.S. The near-beer market in America is still relatively small, but experts see a lot of room for growth. “How can we bring full flavor to a historically bland product?” “With little to no innovation within the nonalcoholic beer category over the past few decades, this poses an exciting opportunity for brewers,” says Golden Road Brewing general manager Dan Hamill. Now, big-box brands and craft breweries are getting into the game, pumping out nonalcoholic options, including lagers, IPAs, and stouts. ![]() □□□ □□□□□□□: Lion | Heidelberg Distributing | Namibia Breweries Ltd | Wine Warehouse California | Columbia Distributing | POSTOBON S.A. | Coca-Cola Beverages South Africa (CCBSA) | Arca Continental | East African Breweries PLC | Distell | Thai Beverage PLC | Asahi Europe & International | Kasapreko Company Limited | Suntory Holdings Limited | Asia Brewery Incorporated | BGI Ethiopia | PT.Not long ago, there were just a couple of nonalcoholic beer brands on the market, none of which offered much in the way of flavor or style diversity. Stringent laws regarding the manufacturing and its compliance to the various regions is set to create hurdles for the Non-Alcoholic Beer Market.Detailed analysis of the Strength, Weakness, and Opportunities of the prominent manufacturers operating in the market will be provided in the Non-Alcoholic Beer Market report.Health- and taste-conscious consumers are increasingly now choosing low- and no-alcohol beer to socialize, drink responsibly and save lives are enhancing the growth of the Non-Alcoholic Beer Market.In 2020, Europe dominated the Non-Alcoholic Beer Market.Furthermore, companies are gaining strong operating margins despite facing challenges related to labelling and less than 1% alcohol content in non-alcoholic beer. During the forecast period 2021-2026, market expansion is poised to be fuelled by increasing attention of consumers to health-issues linked to alcohol abuse urges breweries to expand the assortment of conventional beers through novel drinks concepts. As a result of increasing health-conscious lifestyle trends, demographics, tougher laws, religious prohibitions, and customer preferences, interest in non-alcoholic beers (NABs) has grown steadily, driving market growth. Alcohol-free beer has a maximum alcohol content of 0.05 percent ABV, de-alcoholised beer has a maximum alcohol content of 0.5 percent beer, and low-alcohol beer has a maximum alcohol content of 1.2 percent beer. However, the non-alcoholic variety consists of a little alcohol, this is usually prepared through dealcoholization of carbohydrate by the addition of yeast and other enzymes. Non-Alcoholic Beers, as the name sounds - beer which does not have alcohol. 9/12/2023 0 Comments In this moment concert 2023![]() The upload received over 4.6 million views, prompting an online discussion about filming strangers. A TikToker filmed and uploaded a video of a mans ecstatic reaction at a Beyoncé concert. A Beyoncé fan went viral after a fellow attendee filmed his reaction to the concert. See the tour dates below, and read Heavy Consequence’s 2020 interview with Maria Brink as part of our “Beyond the Boys’ Club” column. Now hes living the surreal experience of going viral. In This Moment are also set to release a new EP titled Blood 1983, commemorating the 10th anniversary of Blood, with details expected to be announced in the coming weeks. Metal outfits In This Moment and Motionless In White will be joining forces in 2023 for an extensive co-headlining tour across America. The Coliseum at Charleston Coliseum & Convention Center. Whereas Ritual hinted at a bluesy sonic sorcery, Mother breathes the activating mantra of an unbreakable spell, commenced on first single “The In-Between.Editor's Pick Beyond the Boys’ Club: Maria Brink of In This Moment Motionless In White & In This Moment: The Dark Horizon Tour. With a total stream tally well past 200 million as of 2020, Ritual elevated them to new creative and critical peaks as well.Īlong the way, they assembled their seventh full-length, the aptly titled Mother with longtime trusted collaborator Kevin Churko. To date, in addition to the Gold-selling album, Blood, the quintet have garnered six Gold and Platinum singles, followed by a trifecta of Top 25 entries on the Billboard Top 200 with Black Widow and Ritual. As millions convened upon the group’s otherworldly and unforgettable concerts, they quietly emerged as one of the most influential and impactful bands of the 21st century. Since coming to life in 2005, In This Moment have presided over a diehard fan base under the watch of “mother” figure and frontwoman Maria Brink-joined by co-founder and lead guitarist Chris Howorth, bassist Travis Johnson, guitarist Randy Weitzel, and Kent Dimmel. MOTIONLESS IN WHITE & IN THIS MOMENT: THE DARK HORIZON TOUR with special guests FIT FOR A KING & FROM ASHES TO NEW. The pair rocked out to Late Night Talking in some brilliant pink feather boas as they sang. Motionless In White are Chris Motionless, Ricky Olson, Ryan Sitkowski, Vinny Mauro, and Justin Morrow. Find In This Moment Camdenton tickets, appearing at Ozarks Amphitheater in Missouri along with Motionless In White, Fit For A King, and From Ashes to New on at 7:00 pm. David Beckham and his 11-year-old daughter Harper seemed to enjoy Harry Styles ’ recent London gig. It’s the dawn of their biggest chapter yet. With guests as diverse as Bryan Garris of Knocked Loose, Caleb Shomo of Beartooth, and video game composer Mick Gordon, Scoring The End Of the World finds the group’s vision magnified wider than ever before with no shortage of teeth, fire, and blood. ![]() The latter debuting at #12 on the Billboard 200 marking the band’s second biggest sales week ever. With over half-a-billion cumulative streams and views to date, they have notched four consecutive Top 5 debuts on the Billboard ‘Top Hard Rock Albums’ chart and ‘Top Rock Albums’ chart with Reincarnate, Graveyard Shift, Disguise, and their latest effort Scoring The End Of the World. Climbing out of the shadows of the rustbelt in Scranton, PA, the group have tirelessly earned the undying allegiance of a devout worldwide audience one record at a time. Motionless In White harnessed the power of an unholy union between industrial metal dissonance, spellbinding gothic pop bombast, and big screen-worthy iconography to emerge as 21st century rock’s most iconoclastic and cinematic force. TICKETS AVAILABLE AT THE ARENA BOX OFFICE OR AT TICKETMASTER.COM There is an 8 ticket limit per household. Event Details TICKETS ON SALE NOW! Plus applicable service charges. 9/12/2023 0 Comments Netflix party on tv![]() You can find all Bustle’s coverage of coronavirus here, and UK-specific updates on coronavirus here.This tip is about the how to Watch Netflix Party on TV using Chromecast. for up-to-date information and resources. If you think you’re showing symptoms of coronavirus, which include fever, shortness of breath, and coughing, call NHS 111 in the UK or visit the CDC website in the U.S. After all, The Office will only be available on Netflix for a little while longer - why let fears of COVID-19 prevent you and your friends from having one final marathon? Of course, none of those options allow users to chat with their friends while all watching the same show, but thankfully, Netflix has thousands of TV shows and movies for you and your friends to plan a socially distant get together around. The following day, Entertainment Weekly reported that Birds of Prey and The Gentlemen would also be available on VOD starting March 24, so people can watch (or rewatch) them at home. On March 16, Universal announced plans to make several of its films - including Emma, Trolls: World Tour and Invisible Man - available to rent on home entertainment, despite their recent or upcoming release dates. Netflix Party is one of the latest ways that people can enjoy some of their favorite movies and TV shows from home in the wake of movie theaters closing due to coronavirus. "You should automatically join the party," the website explains, adding that users can also customize their nickname and photo, in order to make it feel like large group text. Though, to be clear, every user must have their own Netflix account as well.Īfter everyone who wants to join the "party" has downloaded the extension and opened Netflix, it's very easy to get everyone connected: one person clicks on the "NP" in the address bar, and clicks "Start Party." They'll get the URL for the party, which they can send to everyone else, and those users can click on the URL, and then the "NP" button on their own browsers. (Apologies to anyone who uses a different browser thus far, Netflix party is only available for Google Chrome.) Once it's been officially added to the Chrome browser, users can simply open Netflix and begin watching whatever TV show or movie they want. In order to set up a movie night with all of your loved ones, Google Chrome users can download the extension from the official website or the Chrome store. According to the website, the app "synchronizes video playback" for multiple users, so that everyone can watch at the same time (and start from the same point), and has a group chat function that allows the users to talk while watching, even if they're not in the same room. The Chrome extension has actually been around for a while, but in the wake of the CDC guidance for people to stay at home in order to prevent the spread of COVID-19 (the illness caused by the novel coronavirus), Netflix Party has gained an even bigger audience. And here's exactly how to use Netflix Party in order to watch TV with your friends while quarantined in your individual homes. Netflix Party, an app that allows multiple subscribers to stream content in unison, might just be the savior of movie nights everywhere. Social distancing and self-isolation shouldn't get in the way of that Office marathon you've been planning with all of your friends - and now, it might not have to. 9/12/2023 0 Comments Translate tab![]() Human language translators carry the knowledge of different languages, allowing them to read foreign language documents on their own. For the rest of us, though, finding a tool to translate a document or web page into our native language represents an easier process than trying to learn a new language.įoreign language translator tools are available in a variety of places on the Internet. But the most convenient option is to install a Chrome translate extension that will give you results directly in the Chrome web browser. Some of these extensions even help you when learning a new language.īefore we discuss the best Chrome translate extensions, let’s delve into what Chrome can do through Google Translate alone. What Can Chrome Translate on Its Own With Google Translate?įor basic translation work, the Chrome web browser may be able to do the job without the need for additional tools if you have the Google Translate extension available for your version of Chrome. When you encounter a web page in Chrome that uses a foreign language, you may see a popup window that offers to translate the page. (You also can open the Google Translate window by clicking on the GT icon in the right side of the address bar in Chrome.) If not, just right-click anywhere on the web page and left-click on Translate to English in the popup menu. You’ll see tabs for both the current language on the page and your native language (likely English). Click on the tab for the language you want to see. If you would prefer to translate the page into another language, click on the three vertical dots in the Google Translate window and pick Choose Another Language. Select the language you want to use from the drop-down menu that appears. Limitations of Google Translateįor a free tool, Google Translate does a decent job of translating text accurately. Some of the limitations of Google Translate include: It certainly isn’t perfect, but it does an adequate job of translating simple web pages.Mistakes: You shouldn’t count on Google Translate to give you a translation of a legal document or other especially important items.It just isn’t accurate enough to rely on for legally sensitive items versus a human translator. The Translate icon in the address bar will turn blue while you’re viewing a translated web page. It will be automatically translated in the current browser window. This lets Chrome translate specific languages for you in the future. Odd languages: If you are trying to translate an uncommon language, the accuracy of the results drops. Translate Lightning Page Tab Labels in Setup Configure Invocable Actions in Flow Builder More Easily (Beta) Globalization: Data Translation, Plus New and Changed Locale Formats Access Apex-Defined Variables from Outside Flows Run Reports from Einstein Prediction Builder Lightning Flow Management: Prebuilt Report for Screen Flows, Emails. To translate a web page, select the language you want to translate it to and click Translate. By default Chrome’s translating of additionally added languages is turned off, but if you’d rather Chrome handle these languages as well, click more (three dots next to a language) next to the language, and tick the Offer to translate pages in this language setting.Even though Google Translate offers more than 100 languages, quite a few of these will have limited benefits, other than on extremely simple translation jobs. 9/12/2023 0 Comments Finding limits in calculus rules![]() Means for all real ε > 0 there exists a real δ > 0 such that for all x with 0 < |x − c| < δ, we have |f(x) − L| < ε The Math: The Formal Definition Of A Limit No well-supported prediction exists.įor pi, e, and the foundations of calculus, smart minds did the proofs to determine that “Yes, our predicted values get more accurate the closer we look.” Now I see why limits are so important: they’re a stamp of approval on our predictions. For example: Is the number of integers even or odd? The quantity is infinite, and neither the “even” nor “odd” prediction stays accurate as we count higher. We can’t assume one exists, and there may not be an answer to every question. Then ask the “impossible question”: what’s your predicted speed when the gap to the neighboring instant is zero? Limits help answer this conundrum: predict your speed when traveling to a neighboring instant. Speed is funny: it needs a before-and-after measurement (distance traveled / time taken), but can’t we have a speed at individual instants? Hrm. ![]() If we could use an infinite number of rectangles to simulate curved area, can we get a result that withstands infinite scrutiny? (Maybe we can find the area of a circle.) But, if we could make a prediction, is there a single rate that is ever-accurate? It seems to be around 2.71828…Ĭan we use simple shapes to measure complex ones?Ĭircles and curves are tough to measure, but rectangles are easy. We can’t easily measure the result of infinitely-compounded growth. What does perfectly continuous growth look like?Į, one of my favorite numbers, can be defined like this: Nowadays, we have modern limit definitions of pi. It was the precursor to calculus: he determined that pi was a number that stayed between his ever-shrinking boundaries. We can’t measure a shape with seemingly infinite sides, but we can wonder “Is there a predicted value for pi that is always accurate as we keep increasing the sides?”Īrchimedes figured out that pi had a range of What things, in the real world, do we want an accurate prediction for but can’t easily measure?įinding pi “experimentally” is tough: bust out a string and a ruler? Let’s not bring out the math definitions just yet. Limits are a strategy for making confident predictions. This estimate is confirmed by our initial zoom (3:59-4:01, which estimates 9.9 to 10.1 meters) and the following one (3:59.999-4:00.001, which estimates 9.999 to 10.001 meters)”. With these requirements in place, we might say “At 4:00, the ball was at 10 meters. Which one had the ball at 4:00? This ambiguity shatters our ability to make a confident prediction. What happened? We had a sudden jump (a camera change?) and now we can’t pin down the ball’s position. Imagine at 3:59 the ball was at 10 meters, rolling right, and at 4:01 it was at 50 meters, rolling left. Uh oh! Zooming should narrow our estimate, not make it worse! Not every zoom level needs to be accurate (imagine seeing the game every 5 minutes), but to feel confident, there must be some threshold where subsequent zooms only strengthen our range estimate. The predictions agree at increasing zoom levels. With a slow-motion camera, we might even say “At 4:00, the ball was between its positions at 3:59.999 and 4:00.001”. Our prediction is “At 4:00, the ball was between its position at 3:59 and 4:01”. Just grab the neighboring instants (3:59 and 4:01) and predict the ball to be somewhere in-between.Īnd… it works! Real-world objects don’t teleport they move through intermediate positions along their path from A to B. Even so, what’s your prediction for the ball’s position?Įasy. Unfortunately, the connection is choppy:Īck! We missed what happened at 4:00. And if the function behaves smoothly, like most real-world functions do, the limit is where the missing point must be. When our prediction is consistent and improves the closer we look, we feel confident in it. The limit wonders, “If you can see everything except a single value, what do you think is there?”. If we can directly observe a function at a value (like x=0, or x growing infinitely), we don’t need a prediction. But for most natural phenomena, it sure seems to. ![]() Our prediction, the limit, isn’t required to match reality.
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