MATH 19 Final: MATH 19 Final Exam Summer 2017 Solutions

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9 Jan 2019

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Solution: f is continuous at x = 0 if: X2 x2 sin(cid:18) 1 x 0 x2 lim x 0 x 0 x2 x2(cid:19) 1 x2(cid:19) x2 x2 sin(cid:18) 1 x2 sin(cid:18) 1 x2(cid:19) lim x2(cid:19) 0. 0 lim x2(cid:19) = 0. x2 sin(cid:18) 1. Therefore, k = 0 is required for f to be continuous at x = 0. Sample final exam solutions, page 2 of 6. Solution: f is continuous at x = 0 if: continuous at lim x 0 f (x) = lim x 0+ f (x) = f (0) Lim x 0 x + b = cos(0) Next, we want f to be di erentiable at x = 0 d dx (x + b)(cid:12)(cid:12)(cid:12)(cid:12)x=0 d dx (cos(x))(cid:12)(cid:12)(cid:12)(cid:12)x=0. 1 = sin(x)|x=0 1 = 0, which is not possible. Compute the derivative of(cid:0)[sin (f (x))]2 + g(x)(cid:1)1/3 at x = 2. Solution: d dx(cid:0)[sin (f (x))]2 + g(x)(cid:1)1/3 d dx(cid:0)[sin (f (x))]2 + g(x)(cid:1)

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MATH 19 Final: MATH 19 Final Exam Summer 2017 Solutions

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