MATH 365 Final: MATH 365 Amherst S18M365Final
15 Feb 2019
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Read this first: this is a closed-book examination. No books, notes, cell phones, communication devices of any sort, webpages, or other aids are permitted: please give an exact answer when possible. The answer cos(22 ) = . 92718 is ne, while cos(45 ) = . 707 will not get full credit: please read each question carefully. Final exam: [35 points] compute the following derivatives. Do not simplify unless instructed to do so. (a) (b) (c) d d cos3 (cid:19) = dx(cid:0) ln(x) sin(x)(cid:1) = d (cid:18) 2 dx(cid:18)z x et + tan t. 0 dt(cid:19) = (d) (simplify as much as possible) (e) d dx (sec x)x = d dx(cid:16) ln + ln(cid:0) ex(cid:1)(cid:17) : [35 points] compute the following integrals. ln 8. 3 ex dx = ex (a) z tan2 x sec2 x dx = (b) z ln 27 (c) z (d) z (e) z (cid:16) 1 ex e3 dx =
