MATH 121 Final: MATH 121 Amherst S09M12Final

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December 2016 final exam: [32 points] compute the following limits. Be sure to justify your reasoning. (a) lim x 4 (b) lim t 5 x2 4x x2 3x 4. 25 t2 x2 + x (c) (d) lim x 4+ lim x x2 3x 4 x2 4x + 7. 2x2 + 9: [24 points] compute the following derivatives. Do not simplify unless instructed to do so. (a) (b) (c) d dx etan(x) sec(x) + 1! ln(cid:18) x2(3x 5)6 (x2 + 2x)3 (cid:19) d dx. X x d dx: [24 points] compute the following integrals. ( x + 1)x dx. 0 (a) z 1 (b) z 1 (c) z . 1 t t2 dt sin(x) (2 + cos(x))2 dx: [20 points] gasoline is pouring into an upright cylindrical tank of radius 3 feet. When the depth of the gasoline is 4 feet, the depth is increasing at 0. 2 ft/sec.

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