ws32 - WORKSHEET 32 - Fall 1995 1. Find all continuous...

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WORKSHEET 32 - Fall 1995 1. Find all continuous functions f ( x ) satisfying Z x 0 f ( t ) dt =[ f ( x )] 2 + C (Hint: Di±erentiate both sides with respect to x .) 2. Let A betheaverageva lueo f f ( x )= x 3 on the interval [1 , 3]. Determine A , then graph y = f ( x )and y = A on the interval [1 , 3] on the same graph. 3. Suppose f ( x )= 1 2 x +1 . Evaluate the following de²nite integrals: a) Z 3 0 f 0 ( x ) dx b) Z 3 0 f ( x ) dx c) Z 3 0 ± Z x 0 f 0 ( t ) dt ² dx 4. A parabola opens downward, and has roots at 0 and a (here a> 0). a) Suppose the area enclosed by the parabola’s arch and the x -axis is 1. What is the highest point of the parabola in terms of a ? First draw a picture and make a guess. Then compute an answer. b) Suppose the maximum height height of the parabola is 1. What is the area enclosed by the parabola’s arch and the x -axis in terms of a ? Again, ²rst make a guess. 5. a) Find the area of the ²nite plane region bounded by the curve y = x
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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.

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