APPM 1345 Midterm: appm134spring2014exam3_sol
Document Summary
Spring 2014: (10 points) find the 100th derivative of the following functions. (a) f (t) = 7t. Solution: (b) h(x) = ln(13x) + ln(cid:18) 1. 13x(cid:19) (a) f (t) = 7t, f (t) = 7t(ln 7), f (t) = 7t(ln 7)2, f (t) = 7t(ln 7)3, . , f (100)(t) = 7t(ln 7)100 (b) first simplify the function. h(x) = ln(13x) + ln(cid:18) 1. Solution: (a) the y-coordinate at x = e is y(e) = e ln e = e. the tangent slope is y = x ln x. + ln x = 1 + ln x y (e) = 1 + ln e = 2. The equation of the tangent line is y = e + 2(x e) = 2x e. (b) the y-coordinate is y( /4) = (tan( /4))ln( /4) = 1ln( /4) = 1. The tangent slope can be found using logarithmic differentiation: y = (tan x)ln x.
