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Unformatted text preview: x y z that lie inside of the sphere of radius 1, and which satisfy 0 x 3. ind the volume of S . Problem 3. Give an example of a function f x for which the trapezoidal rule approximation with n 2 to the integral 1 f x dx is exact (i.e., the error is zero), while the trapezoidal rule approximation to the same integral with n 4 gives a nonzero error. (No formula is necessary; a graph of the function, with explanations, will sufFce). Problem 4. Compute the integral e x e x dx . Problem 5. Let f x x 2 1, x 0. (a) Show that f is one-to-one on ; (b) compute the inverse of f x ; (c) Fnd the derivative of the inverse of f x at the point 2. Problem 6. Graph the function f x e x e x . 1...
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This note was uploaded on 02/22/2010 for the course MATH Math 31B taught by Professor Houdayer during the Fall '09 term at UCLA.
- Fall '09