1910fa17-prelim2-review-solutions.pdf - P RELIM 2 R EVIEW N...

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PRELIM2 REVIEWNAME:SOLUTIONSMath 1910Warning:These problems are by no means a comprehensive representation of the material that might appear on theexam. That is, there may be topics not covered by these problems that you are still responsible for knowing. Let theseproblems be a supplement to your preparation for the exam, but be sure to review other sources (e.g. your notes,homework assignments, and the textbook) as well.(1) Find the derivatives of the following functions.(a)f(t) = (sin2t)tSOLUTION: Lety= (sin2t)t. Then ln(y) =2tln(sint). Now use implicit differentiation.
(c)h(t) =x2-1ex
(2) Find the following definite or indefinite integrals.(a)Z(sinx)(coshx)dx
(b)SOLUTION: Use the identitycosh2(t) -sinh2(t) =1and solve forcosh2(t). Then use
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