126RECEX5 - dt 5 Let f x = Z √ x 2 sin t t dt x 2(a Find...

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MAT 126: Calculus B — Recitation Exercise Sheet #5, Fall 2009 1. Use the Fundamental Theorem of Calculus to find the derivatives of the following functions. (a) f ( x ) = Z x 1 cos(2 t ) dt (b) f ( x ) = Z x 2 1 sin( 1 2 t ) dt (c) f ( x ) = Z 2 e x ln( t ) dt (d) f ( x ) = Z x π/ 4 tan - 1 ( t ) dt 2. Use the Fundamental Theorem of Calculus to find the derivative d dx . f ( x ) = Z ln x x 2 ( e 2 t - t 2 ) dt 3. Use the Fundamental Theorem of Calculus to find the derivative d dx . f ( x ) = Z 3 x 2 x t 2 - 1 t 2 + 1 dt 4. Determine if the given function has any maxima or minima. Classify whether they are local or global. g ( x ) = Z x 0 ( t 4 - t
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Unformatted text preview: ) dt 5. Let f ( x ) = Z √ x 2 sin t t dt + x 2 . (a) Find f ( x ) (b) Find f (4) 6. Find a function f and a number a such that for x, 1 + Z x a tf ( t ) dt = x 3 . 7. Find the derivative f ( x ) of the function f defined as follows: f ( x ) = Z x 2 √ 1 + t 2 dt. (a) Find the intervals on which the function f is increasing or decreasing. (b) Find the intervals on which the function f is concave up or concave down....
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