MATH 19A Study Guide - Midterm Guide: Intermediate Value Theorem, Inflection Point, Radar Gun
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Good luck and have a great winter break: (30 points) compute the derivatives :~ of the following functions (no need to simplify): (a) y = e tan x (b) y = vsinh(wx) where w is a constant. 1 (d) y = in(k2 + sec 5 + e2(371")) where k is a function that does not depend on x. 2: (15 points) (a) state the intermediate value theorem. (b) show that sinh2 (x) = x has at least two real solutions. (c) show that sinh2(x) = x has exactly two real solutions. X. r(x) or rex) or both tell you about the shape of the graph of f(x) = sinh 2(x) 3: (10 points) find an equation of the tangent line at the point (3,1) to the lemniscate (which looks like the infinity symbol 00) given by. 2(x 2 + y2)2 = 25(x2 _ y2: (10 points) find the absolute extrema of f(x) = ~ where 1 ::; x ::; 5.
