MATH 220 Midterm: MATH 220 KSU S10Fin
15 Feb 2019
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1: calculate the following limits: (a) (8 points) lim x 3. X + 1 2 x 3 (b) (8 points) lim x . 9x2 + 16 x + 7 (c) (9 points) lim x 0 sin x x x4 + x3. 2: obtain the following information and use it to sketch the graph of f : f (x) = Write none when appropriate. f (x) = 2x (x2. 9)3 . (b) (4 points) the vertical asymptotes. The horizontal asymptotes (c) (4 points) the intervals where f is increasing: , decreasing: (d) (3 points) location of the local maxima: , local minima: (e) (4 points) f is concave upwards: , concave downwards: (f) (4 points) use this information to sketch the graph of f . 4: di erentiate the following (do not simplify your answers): (a) (9 points) y = 3 x2 + x tan x + e3 (b) (8 points) f (x) = x3 + 3.
