Practice Midterm 1 Solutions - 1 Mathematics 19B Winter...

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1 Mathematics 19B; Winter 2002; V. Ginzburg Practice Midterm I, Solutions 1. For each of the ten questions below, state whether the assertion is true or false : (a) cos x dx = sin x + C (b) 7 7 2 (c) b a f ( g ( x )) g ( x ) dx = b a f ( u ) du (d) The area of the region bounded by the curves y = x 3 - 14 x 2 - 8 x + 4, y = 6 x 2 - 5, x = 3, and x = 7 is - 143 (e) If b a f ( x ) dx is negative, then f ( x * ) < 0 at some point a x * b (f) d dx x 0 f ( t ) dt = f ( x ), provided that y = f ( x ) is a continuous function. (i) Let f ( t ) be the rate of growth of a population. Then b a f ( t ) dt = F ( b ) - F ( a ), where F ( t

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