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![]() If the antiderivative F of f is known, then the definite integral of f is calculated as follows I) Main Theorem of the Differential and Integral Calculations. H) If a function f is continuous and differentiable, then applies ∫ a b f ( x ) g ( x ) dx = f ( a ) ∫ a μ g ( x ) dx + f ( b ) ∫ μ b g ( x ) dx G) Second Mean Value Theorem If f is monotonic and bounded and g integrable, then there exists at least one number μ for which the following relationship is valid. ∫ a b f ( x ) g ( x ) dx = μ ∫ a b g ( x ) dx ∫ a b f ( x ) dx = ∫ a c f ( x ) dx + ∫ c b f ( x ) dxĮ) Mean Value Theorem If f is integrable and we have m ≤ f ≤ M, then there exists at least one number μ with m ≤ μ ≤ M and we have the following relationship.į) General Mean Value Theorem If f and g are integrable and we have m ≤ f ≤ M and g ≥ 0 either always or g ≤ 0, then there exists at least one number μ with m ≤ μ ≤ M and it works as follows. ![]() ∫ a b f ( x ) + g ( x ) dx = ∫ a b f ( x ) dx + ∫ a b g ( x ) dxĭ) Decomposition of the definite integral in part integrals. There are a, b, c ∈ ℜ constants.Ī) Interchange of the limits of integration.ī) Factor Rule A constant factor a can be pulled outside the integral.Ĭ) Sum Rule A sum under the definite integral can be integrated by means of the summands. The existence of the integrals in each case provided. Rules of calculation of definite integrals ∫ ( f ( g ( x ) ) g ′ ( x ) ) dx = ∫ f ( z ) dz ∫ ( u ( x ) v ′ ( x ) ) dx = u ( x ) v ( x ) - ∫ u ′ ( x ) v ( x ) dxį) Substitution If the function f(z) is continuous and z = g(x) is differentiable, then the following relationship holds. ∫ f ′ ( x ) f ( x ) dx = ln | f ( x ) | + CĮ) Integration by parts Are the functions u(x) and v(x) are differentiable, then the following relationship holds. ∫ f ( a x + b ) dx = 1 a F ( a x + b ) + Cĭ) If f(x) is differentiable and f(x) not equal to 0, then the following relationship applies. ∫ ( f ( x ) + g ( x ) ) dx = ∫ f ( x ) dx + ∫ g ( x ) dxī) Factor Rule A constant factor a can be pulled out of the integral.Ĭ) If F(u) is the antiderivative of f(u), then the following relationship holds for arbitrary constants a and b with a not equal to 0. The concept here is exactly the same as what is used when doing u-substitution (URL to video below if you need it).Calculation Rules for undefined IntegralsĪ) Additivity A sum under the integral is integrated by the summands are integrated separately and then summed. At least, that's how it clicked for me.Īs far as the manipulating differentials goes, it's true that you can't just treat differentials like they are normal terms in an equation (as if dx were the variable d times the variable x), but it is legal to split up the dy/dx when differentiating both sides of an equation. If you are used to the prime notation form for integration by parts, a good way to learn Leibniz form is to set up the problem in the prime form, then do the substitutions f(x) = u, g'(x)dx = dv, f'(x) = v, g(x)dx = du. Basically, the only difference is that the "video form" uses prime notation (f'(x)), and the "compact form" uses Leibniz notation (dy/dx). The "compact form" is just a different way to write the form used in the videos. I suspect however, with more practice, exposure and careful consideration, you will get it on your own. ![]() You may want to suggest to the Khan site to make a video talking about the the conversion and utility of the long form to short form notation. These articles really just serve to confirm the ubiquity of the short form notation and they may help you get you more comfortable with it: ![]() This article talks about the development of integration by parts: Same deal with this short form notation for integration by parts. Now, since both are functions of x, for short form notation we can leave out the x. Sal writes (in the intro video)ĭ/dx = f'(x) For a moment, consider the product rule of differentiation. ![]() ![]() ![]() When the N1A’s Ethernet LEDs and front panel display were turned off, and up-sampling on my streamer/DAC enabled, things got even better. Especially the better dynamics and an 3-dimensionality to the music which has always been one of the key missing factors with my Xserve (when compared to my disc transport). With some longer term listening of just the N1A across a couple of days then switching back to my Xserve, the differences were much more pronounced/discernible. I use cautionary adjectives because when I did quick/immediate A/B comparisons against my dedicated (Apple) Xserve, those attributes seemed almost the same, but kinda, almost/not quite… Let me just cut to the chase here, my initial reaction to the N1A’s sound was “Wow!”… Seems to have an incredible sense of effortlessness, an apparent improvement in dynamics, and definitely less grainy sounding/cleaner, and what seemed like quieter background. There are quite a few reviews online, but none that really go into much depth, so, here’s a slightly more comprehensive look at the N1A… there’s just so much to play with this thing, sorry this post is going to be a little long :P… but hopefully useful for others seriously considering the Melco. Just spent the last couple of days playing around with it. Another Christmas holiday, another little project D… While spending time in the UK recently, I couldn’t resist picking up a Melco N1A. ![]() ![]() A computer-generated AOC in a bikini is just the tip of the iceberg: unless we start talking about algorithmic bias, the internet is going to become an unbearable place to be a woman. And they are also used to create huge amounts of deepfake porn. And, last year, an algorithm used to determine students’ A-level and GCSE grades in England seemed to disproportionately downgrade disadvantaged students.Īs for those image-generation algorithms that reckon women belong in bikinis? They are used in everything from digital job interview platforms to photograph editing. Racist facial recognition algorithms have also led to black people being arrested for crimes they didn’t commit. Back in 2015, for example, Amazon discovered that the secret AI recruiting tool it was using treated any mention of the word “women’s” as a red flag. And this is not an academic issue: as algorithms control increasingly large parts of our lives, it is a problem with devastating real-world consequences. The study is yet another reminder that AI often comes with baked-in biases. Why was the algorithm so fond of bikini pics? Well, because garbage in means garbage out: the AI “learned” what a typical woman looked like by consuming an online dataset which contained lots of pictures of half-naked women. (After ethical concerns were raised on Twitter, the researchers had the computer-generated image of AOC in a swimsuit removed from the research paper.) For some reason, the researchers gave the algorithm a picture of the Democratic congresswoman Alexandria Ocasio-Cortez and found that it also automatically generated an image of her in a bikini. When you fed the same algorithm a similarly cropped photo of a woman, it auto-completed her wearing a low-cut top or bikini a massive 53% of the time. Researchers fed these algorithms (which function like autocomplete, but for images) pictures of a man cropped below his neck: 43% of the time the image was autocompleted with the man wearing a suit. Take a look and prepared to be blown away by some of these flabbergasting cheerleader wardrobe mishaps. The list below provides some insight on hilariously shocking cheerleader uniform faux pas. Fashion Nova is currently selling the controversial 'Butterfly Babe Thong 2 Piece Bikini', but there's backlash over the barely-there thong bottoms that critics claim is inappropriate for the beach. That is my stripped-down summary of the results of a new research study on image-generation algorithms anyway. Due to the physical exertion involved with cheering because of the running, flipping and splitting, it can cause a variety of wardrobe malfunctions. ![]() ![]() There are so many of these pictures online, in fact, that artificial intelligence (AI) now seems to assume that women just don’t like wearing clothes. W ant to see a half-naked woman? Well, you’re in luck! The internet is full of pictures of scantily clad women. ![]() ![]() ![]() This information can be found in the System Requirements section of a product’s website. There are also some that don’t require a powerful computer, while others need a newer model computer and plenty of available RAM. There are options on our list for Windows, Mac, and Linux. Next, make sure the free Photoshop alternative you want will work on your device. However, if you have spotty internet, or like to edit while you travel or commute, you will need downloadable software that doesn’t require an internet connection. It’s also a good choice if you like to edit photos over multiple devices. If you have an older computer or don’t have much space on your hard drive, an online option could be the way to go. The first thing you should decide is whether you want an online option or a downloadable free Photoshop alternative. With 15 excellent free Photoshop alternatives on our list, how can you choose the right software to edit photos the way you need? Read on for some key things to look for when choosing a free alternative to Photoshop. How to Choose the Best Free Photoshop Alternative Top 3 Free Photoshop Alternatives Snapshot Download the Best Alternative to Photoshop for Free.Best Free Photoshop Alternatives Comparison Chart.15 Free Photoshop Alternatives With Similar Features in 2023.How to Choose the Best Free Photoshop Alternative.Top 3 Free Photoshop Alternatives Snapshot.This article introduces the 15 best free Photoshop alternatives and compares their features, benefits, and drawbacks. ![]() In addition, most of these offer free stock images, something even paying for a pricey Photoshop or Adobe Creative Cloud subscription won’t get you. Thankfully, several excellent free alternatives to Photoshop offer similar features without the high price tag and steep learning curve. Many people consider Photoshop the best photo editor, but unless you have experience and dedicated training with this program, you will find it hard to use and cost-prohibitive.Ĭontent creators and photographers need easy-to-use, free Photoshop alternatives that allow them to navigate tools and features quickly to post more photos in less time. ![]() If you've ever tried to edit a photo with Photoshop, you know how intimidating and complicated the software can be. ![]() ![]() ![]() ![]() ![]() Chance is likely to contribute less on the second time we measure performance. When the measurements are extreme, they are likely to be partly caused by chance. All measurements are made up of one true part and one random error part. Why? Testing measurements can never be exact. Extreme performance tends to get less extreme the next time. Our performance always varies around some average true performance. Their true ability perhaps hasn’t changed. And there could be many reasons for their earlier performance - stress, fatigue, sickness, distraction, etc. Since these individuals were measured as being on the low end of the scale of skill, they would have shown an improvement even if they hadn’t taken the skill-enhancing program. Their higher scores could be the result of regression to the mean. John’s conclusion: “The skill-enhancing program caused the improvement in skill.” This isn’t necessarily true. Their scores are now higher than they were on the first test. In Seeking Wisdom, Peter Bevelin offers the example of John, who was dissatisfied with the performance of new employees so he put them into a skill-enhancing program where he measured the employees’ skill: The rule goes that, in any series with complex phenomena that are dependent on many variables, where chance is involved, extreme outcomes tend to be followed by more moderate ones. The notion of regression to the mean was first worked out by Sir Francis Galton. One of the errors that he examines in Thinking Fast and Slow is the infamous regression toward the mean. It turns out there is a whole set of logical errors that we commit because our intuition and brains do not deal well with simple statistics. Nobel prize-winning psychologist Daniel Kahneman wrote a book about biases that cloud our reasoning and distort our perception of reality. Learning about regression to the mean can help us. It is important to minimize instances of bad judgment and address the weak spots in our reasoning. Learning to recognize when regression to the mean is at play can help us avoid misinterpreting data and seeing patterns that don’t exist. Regression to the mean is a common statistical phenomenon that can mislead us when we observe the world. ![]() ![]() ![]() Step 1: Open the Configuration Settings from the XAMPP Control Panel If you’re using a Windows device, you can follow these four steps to update your default port settings in XAMPP. How to Fix the XAMPP Error “Apache Shutdown Unexpectedly” in Windows Get started with DevKinsta today, even if you’re not a Kinsta customer. Looking for a free and powerful local WordPress development tool? DevKinsta features quick and easy site creation, email and database management tools, one-click PHP version switching, and full integration with MyKinsta. We will provide instructions for both operating systems below, starting with Windows. Also, the interface may look a bit different depending on the XAMPP version you’re using. However, the method for resolving the error varies slightly between Windows and macOS. In any event, the easiest fix is to simply modify the XAMPP default settings. Additionally, you may notice that the error message indicates the problem may also be attributed to “missing dependencies, improper privileges, a crash, or a shutdown by another method.” ![]() Usually, it means that another application installed on your computer, such as Skype, is using the same port as XAMPP. This message is most commonly caused by a blocked port. However, what may be new to you is the “Apache shutdown unexpectedly” error you’re seeing. If you’re reading this article, we’ll assume you’re already at least somewhat familiar with XAMPP. ![]() Optimize your admin tasks and budget with $275+ enterprise-level features included free in all WordPress plans. ![]() ![]() ![]() ![]() Title: Quality Assurance Assistant Company: Psd Afloat West San Diego. If any questions arise related to the accuracy of the information contained in translated text, refer to the English version on this website, it is the official version. Find James Collingss phone number, address, and email on Spokeo. The official text of content on this site is the English version found on this website.Users are advised to use MS Edge, Safari, Chrome, or Firefox browser to take full advantage of the Google Translate feature. IE users: Please note that Google Translate may not render correctly when using Internet Explorer.Any individuals or parties that use Commander, Navy Region Southeast, content in translated form, whether by Google Translate or by any other translation services, do so at their own risk. units shore-based support and Personnel Specialist. • All site visitors may choose to use similar tools for their translation needs. PSD Afloat West is a Navy initiative to provide specified Fleet. Commander, Navy Region Southeast, does not directly endorse Google Translate or imply that it is the only language translation solution available to users.Some items cannot be translated, including but not limited to image buttons, drop down menus, graphics, photos, or portable document formats (pdfs).Commander, Navy Region Southeast, does not warrant the accuracy, reliability, or timeliness of any information translated.This service is meant solely for the assistance of limited English-speaking users of the website.The automated translations should not be considered exact and should be used only as an approximation of the original English language content.Commander, Navy Region Southeast, has no control over the features, functions, or performance of the Google Translate service.Google Translate, a third party service provided by Google, performs all translations directly and dynamically. Visual arts education in photography, drawing, painting, 2D graphic design, ceramics, sculpture, jewelry, metals and 3D design. ![]() ![]() So let's say I want to print everything from the 5th line in the text file Haruki.txt then, I will use the following command: tail -n +5 Haruki.txt 3. To do so, you'd have to use the -n flag and append the line number from where you want to print the file with the + sign: tail -n + So if you want the output from a specific point, this can be very handy. You can also use a number higher than 10 here. To print the desired number of last N lines, all you have to do is use the -n flag and append the number of the last N lines you want to be printed: tail -n įor example, here, I printed the last three lines of my text file named Haruki.txt: tail -n 3 Haruki.txt Print the last N linesĪs I mentioned earlier, the tail command prints the last ten lines by default but you may not always want the same behavior. This indicates that you need to replace the content along with with a suitable value. You’ll see some command examples with text inside. South of the Border, West of the Sun (1992)Ĭolorless Tsukuru Tazaki and His Years of Pilgrimage (2013)Īnd when the tail command is executed without any options, it prints the last 10 lines of the file: Hard-Boiled Wonderland and the End of the World (1985) To make things easy to understand, I will be using the Haruki.txt text file containing the following line: Hear the Wind Sing (1979) is where you'd enter the file name that you want to pair with the tail command.allows you to tweak the default behavior of the command.To use any command in the terminal, execution of the command in the right syntax is compulsory, so let's start with its syntax first. ![]() New to the terminal? Learn the terminology How to use the tail command in Linux ![]() |