For each of the ten questions below, state whether the...

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1 Mathematics 19B; Winter 2002; V. Ginzburg Practice Midterm I 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 2 cos 3 x dx = 1 3 (sin 3 x + 13) | 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 12 . (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. (g) lim n →∞ 1 n n j =1 sin ( π j n ) = π 0 sin x dx . (h) lim n →∞ 1 n n j =1 ( 1 + j n ) 2 = 1 0 x 2 dx . (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 ) is the population as a function of time. (j) x 0 sin t dt

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