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Unformatted text preview: Math 210 Exam 3 Review Sections 4.2 4.4 and 5.1-5.5 1) Find the limits a) x x x cos sin 1 lim 2- b) 3 2 lim x e x x c) x x x ln tan lim + d) x x x ) 2 ( sin lim 1- 2) For the functions below, use the first and second derivatives to find where f is increasing, where f is decreasing, where f is concave up, and where f is concave down. a) 3 12 5 ) ( x x x f- + = b) x xe x f 3 ) ( = 3) Find any relative extrema for the functions below using either the First Derivative Test or the Second Derivative Test. a) 2 3 ) (- + = x x x f b) x x e e x f- = 2 ) ( c) 3 1 3 ) ( x x x f +- = 4) For the function 3 4 3 1 3 6 ) ( x x x f + = , find the location of any horizontal tangent lines or vertical tangent lines. Anywhere there is a vertical tangent line, determine if there is a cusp or a point of inflection there. 5) Graph a function that satisfies all of the following conditions f is continuous for x f (-1) = 3 f (3) = 2 2 ) ( lim = - x f x...
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