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We have claimed that a randomly generated point lies on the equator of the sphere independent of where we pick the North Pole. To test this claim randomly generate ten vectors in 128 dimensions whose coordinates have value ±1. Think of these ten vectors as ten choices for the North Pole. Then generate some additional random vectors with ±1 coordinates. For each of the new vectors determine how many of the original vectors they are close to being perpendicular to. That is, they lie close to the equator.
The Mean Value Theorem Assume f(x) is a function that satisfies both of the subsequent. 1. f(x) is continuous on the closed interval [a,b]. 2. f(x) is differentiabl
greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t,s)= {1-s for t or equal to s
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Example for Comparison Test for Improper Integrals Example: Find out if the following integral is convergent or divergent. ∫ ∞ 2 (cos 2 x) / x 2 (dx) Solution
tom has 150 feet of fencing to enclose a rectangular garden. if the length is to be 5 feet less than three the width, find the area of the garden
A farmer's rectangular field has an area in which can be expressed as the trinomial x2 + 2x + 1. In terms of x, what are the dimensions of the field? Because the formula for th
Computing Limits :In the earlier section we saw that there is a large class of function which allows us to use to calculate limits. However, there are also several limits for whi
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How to Solve Inequalities ? Now that you have learned so much about solving equations, you're ready to solve inequalities. You might think that since an equation looks like
Evaluate the following integral. ∫ (x+2 / 3√(x-3)) (dx) Solution Occasionally while faced with an integral that consists of a root we can make use of the following subs
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