math111_2003fall_prelim3

# math111_2003fall_prelim3 - Math 111 Prelim 3 Nov 20 2003...

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Math 111 (Fall 2003) Prelim 3 (11/20/2003) 2 1. [16pts (4pts each)] (a) Find the most general anti-derivative for f ( x ) = 8 x 3 + e x - sin( x ). 2 x 4 + e x + cos x + C (b) Find the most general anti-derivative for g ( x ) = x 2 + 3 x 3 x . x 2 2 + x 3 + C 1 for x < 0 x 2 2 + x 3 + C 2 for x > 0 (c) Compute 2 0 1 - x 2 dx . 2 0 1 - x 2 dx = 1 0 (1 - x 2 ) dx + 2 1 - (1 - x 2 ) dx = x - x 3 3 1 0 + - x + x 3 3 2 1 = 1 - 1 3 - 2 + 8 3 + 1 - 1 3 = 2 (d) Compute e 8 e 2 dx x . e 8 e 2 dx x = ln x | e 8 e 2 = ln e 8 - ln e 2 = 8 - 2 = 6 CONTINUE TO THE NEXT PAGE
Math 111 (Fall 2003) Prelim 3 (11/20/2003) 3 2. [4pts] Express the following limit as a definite integral on the given interval lim n →∞ n i =1 x * i Δ x, [1 , 4] . (Note: You only need to write the integral, you do not need to evaluate it.) 4 1 x dx 3. [10pts (5pts each)] A Volvo S70 T5 accelerates from a dead stop with its velocity constantly increasing. The table below gives its velocity at several time intervals.

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• Fall '06
• MARTIN,C.

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