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handout_11_25 - MATH 1A THE FUNDAMENTAL THEOREM OF CALCULUS...

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Unformatted text preview: MATH 1A: THE FUNDAMENTAL THEOREM OF CALCULUS 1. Let f (t) be the function defined on the interval [-5, 5] by the graph shown. Define the area function F by f x 4 2 x F (x) = 0 f (t) dt. 5 3 1 2 1 3 5 x (1) Where is F increasing and decreasing? (2) Where is the absolute maximum and the absolute minimum of F ? (3) Where are the local extreme points? (4) Where is F concave up and concave down? (5) Where are the inflection points of F ? Date: November 25, 2009. 1 2. (1) Find the derivative of 0 x 1 dt, 1 + t2 where x = 0. (2) Find the derivative of 1/x 0 1 dt, 1 + t2 where x = 0. (3) Find the derivative of 1/x 1 1 dt + dt, 2 1+t 1 + t2 0 0 where x = 0. Conclude that F (x) is constant on (-, 0) and constant on (0, ). x F (x) = (4) Evaluate the constant value(s) of F (x). 2 ...
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handout_11_25 - MATH 1A THE FUNDAMENTAL THEOREM OF CALCULUS...

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