Evaluate the integral x 3 1 x 2 1 dx a 4 b 2 c d 23 e

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14. Evaluate the integral x 3 1 ! x 2 0 1 " dx a) ! /4 b) ! /2 c) ! d) 2/3 e) # f) 1 Ans: d 15. Solve the differential equation. x y y 5 7 = ! 16. Find the average value of f ( x ) = sin 2 x cos 3 x over the interval [– ! , ! ] 17. Consider the sequence defined by a n = ( ! 1) n + n ( ! 1) n ! n . Does this sequence converge and, if it does, to what limit? Ans a 18. Find the area of the surface obtained by rotating the curve y = 1 4 x 2 1 2 ln x , 1 ! x ! 2 about the y -axis. a. 2 101 ! b. 99 2 ! c. 48 ! d. 24 ! e. 12 ! f) none of these
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Ans: f
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19. Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the largest range of values of x for which the given approximation is accurate to within the stated error. 2 4 cos 1 , | | 0.08 2 24 x x x error ! " + < 20. Find a series representation for e x x dx ! . ! " + C ! " ! " ! " ! "
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