MATH137 : assign7.pdf

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: John- Paul Pretti

Document Summary

4 x2, [ 1, 2] (b) f (x) = x (c) f (x) = e x e 2x, [0, 2: find the linearization l2(x) of f (x) = x. 1 + x2 at a = 2: use the linear approximation to estimate the given number. (a) 100. 2 (b) (2. 998)5: use the fact that d (2 x) ln(2 x) has at least one solution in the interval (0, 1). dx[x ln(2 x)] = ln(2 x) x. 2 x to show that the equation x : consider a function f and a point a. Suppose that there is a number k such that g(x) = f (a) + k(x a) satis es x a. Prove that f is di erentiable at a and f(cid:48)(a) = k. lim x a. = 0 f (x) g(x: use the mean value theorem to prove that.