MATH 142 Midterm: MATH 142 Exam 1 Solutions
Document Summary
Problem 1. (10pts) compute problem are not required to give an explanation in english. dx (cid:16)(x2 + x)sin 1(x)(cid:17). You must of course show your work, but for this d. Then ln y = ln(x2 + x)sin 1(x) = sin 1(x) ln(x2 + x). We used, of course, the rules for di erentiating ln x and sin 1(x) as well as the product rule. 2x + 1 x2 + x(cid:19) = (x2 + x)sin 1(x)(cid:18) 1 x2 ln(x2 + x) + sin 1(x) 2x + 1 x2 + x(cid:19) . (cid:3) Problem 2. (10pts) compute the volume of the solid obtained by rotating the region bounded by 0 y e2x x2 and 0 x 1 about the line x = 1. If you know a formula to compute volume (and you should), there is no need to develop the formula from scratch using a limit. We use shells, the formula for which is.
