MATH 152 Midterm: MATH 152 TAMU 2015a X2H Solutions
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Thu, 02/apr c(cid:13)2015 art belmonte dx by hand using w = x: compute z . X + x x (check answer with calculator. : let w = x. When x = 1, w = 1; as x , w . 2w w + w3 dw = z . 2 1. 57: use the comparison theorem to determine whether the integral z . Show your work by hand; check on your calculator. Since the integral dx = 2 3. 54 (see below) is nite, so sin2 x x: note that 0 sin2 x x 1 x for 0 < x . R : here are details for the comparison integral. dx by a comparison theorem. = 2 0 = 2 a: solve the initial value problem dy y (0) = 0, explicitly for y by hand. (check with calc. , the differential equation is separable. 1 p1 y2 dy = 2x dx sin 1 y = x2 +c.
