MATH 1120 Midterm: MATH 1120 Cornell WARMUP2018 Exam Winter 4 24Solutions
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The integrand has a vertical asymptote at x = 0. A complete solution would be to also write the correct calculation: 0 and neither integral converges separately by a direct calculation. 1 dx (x 5)(x + 10)(x + 12) (b) z 1. The integrand is continuous in the closed interval [ 1, 1]; the integral is proper. By ftc the function has an antiderivative f (x), and the integral equals f (2) f ( 1). Give a very brief reason. (a) z 1. Converges by a direct calculation. (b) z . Hint: compute the limit of the integrand as x . The function f (x) has a vertical asymptote at x = 1. So you must write p(x 1)(x + 2) X 1 dx converges by direct calculation, the rst integral converges. For the second f (x) = x + 3 x x. 1 + 3/x p(x 1)(x + 2) p(1 1/x)(1 + 2/x) f (x) = 1.
