The area function can calculate an area (a) above the curve (b) below the curve or (c) both above and below. A couple of very useful online calculators: This Desmos calculator will show you the different shadings for any function; You’ll want to make this your first step as it will...
You can’t always use a table or calculator in class; Sometimes you have to make a more formal approach, using the definition of a limit. The following example shows how to do this for the function y = 2x + 2. Slightly different steps are needed to solve for infinity, and values othe...
We surf the web daily, and as developers, we tend to notice subtle details on a website. The one thing I take note of all the time is how smooth the animations on a website are. Animation is great for UX and design purposes. You can make an interactive website that pleases the vis...
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Let's make something clear: for all intents and purposes, a 1540+ on an SAT is equivalent to a perfect 1600. No top college is going to give you more credit for a 1580 than a 1550. You've already crossed their score threshold, and whether you get in nowdepends on the rest of you...
Use the graphs to make a conjecture about the relationship between the functions. f (x) = sin x + cos (x + pi / 2), g (x) = 0 Consider a graph J(x) = -2 \sin 4x. How to check if the origin is an x-intercept for it? Compared ...
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This function is trying to get to its limit of -1 (red dashed line), even if it doesn’t quite get there. Generally speaking, a limit puts some kind of boundary in place: a point where you can’t (or shouldn’t) go any further. For example, a maximum speed limit of 75 m.p....
Bernstein polynomial approximating a curve. In many situations, it’s better to use Bernstein polynomials rather than anexplicit functionof the form y = f(x), because of the limitations offunction notation. These include the fact that a vertical line (i.e. avertical asymptote) x = c cannot...