APPM 1350 Midterm: appm1350spring2013exam2_sol
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Spring 2013 (b) on what intervals is f increasing? decreasing: (15 points) (a) find the linearization of f (x) = 4 1 x at x = 0. (b) use the linearization to approximate the value of 4 0. 92. Solution: (a) first nd the values of f (0) and f (0). f (x) = (1 x)1/4 f (0) = 1 (1 x) 3/4 = 4(1 x)3/4 f (x) = f (0) = . 4 x (b) note that 4 0. 92 = f (0. 08) l(0. 08). Solution: (a) f is not de ned at x = 3 so we check at these x-values for asymptotes. lim x . So there are vertical asymptotes at x = . = lim x x2 x2 2/x (1 3/x2) x2 2/x (1 3/x2) x2. So there is a horizontal asymptote at y = 0 . (x2 3)2 > 0 so f is always increasing where de ned on.
