Find the Limit of a Sequence Subsequential Limit. Technology Find Limit of Sums on the TI 89 What is a Limit? A limit is a number that a function approaches. For example, take the function f(x) = x + 4. If you evaluate the function at x = 5, the function equals: f(5) = ...
Step 2: Find the slope for the line segment between the next two points =(y3 − y2)/(x3 − x2) = (32 − 12)/(4 – (-1))= 20/5 = 4. Step 3: Compare the slopes you calculated in Steps 1 and 2. The two slopes equal 4, so the points do show collinearity. Linear ...
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Check out this Desmos graphic to see this interactively. I admit I often come to play with it when I need to refresh my understanding of the two products. It is crucial that you have a basic intuition about the dot and cross products if you are to follow the rest of this tutorial. I...
Find all the points on the graph of y = e^x \sin x at which the slope is zero. Sketch on the same axes the following functions \begin{alignat}{3} y &=&& 3\tan x, \\ y &=&& \tan \left(x-\pi/2 \right), \\ y &=&& \s...
Find the area of the shaded region below, if the radius of the circle is 5. This is a classic SAT type question. You might already know how to solve it. But it's unlikely you ever ran into something like this in school. The first time you see this, it might be confusing. How d...
If you click on it it gives you the opportunity to label the axes. Maybe I'll get around to re-drawing those graphs with the free online utility https://www.desmos.com/calculator and label them this time. It's a nice utility. Anybody can go there and have functions you...
Mathematically, you find them by looking at thederivative. At an extreme point, where there is a direction change, the derivative of the function is zero. Note: thederivativeis the slope of thetangent line. In the above graph, the tangent line is horizontal, so it has a slope (derivative...