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Midterm 1 Calculus I (12010-007) Answer the questions in the spaces provided. Show your work. Name: ID:U Question: 1 2 3 4 5 6 Total Points: 15 15 10 20 30 10 100 Score: 1. Find the following limits. (a) 5 points lim x*i (b) 5 points 2 + 4r 5 x 8x + 7 urn n—*+ — c-u - — 3 + 4n 8n 2 +5 k 0 —. t ci) c cf -r cD cJD . — riD C C C-) bID C ci) C C C.) CI + cD cD - LCD . -e t i/ 2 N 0 ft ci) biD 2x 1 (b) 10 points f(x) = — 2x2 if < —1 2 atx=—1 —i if —1<x<0 2x2_3 ifx>0 Jv- N) (_7 - L c\,\ (-fç,’3 ,)-:: j’ ‘k_) c: —\ V S Qt& h .- (2sinx if x 0 3. 10 points Verify that the function f(x) = is discontinuous at x = x 0 atx=O 0. Is it a removable discontinuity? If so, remove the discontinuity and redefine the function so that it is continuous. ‘—? w) ()D ) , Page 3 4. (a) 5 points Find the equation of the tangent line to the curve y point (1,1/5). = 2 x+4 at the — ‘)\ ) 2 ‘ I — 4 - (b) 5 points Find all points on the graph of horizontal. Page 4 = — 2 where the tangent line is (c) 10 points A particle travels as a function of time according to the formula s . where s is in meters and t is in seconds. Find the velocity 3 100 + lOt + O.01t and acceleration of the particle at t = 2. S: O-kOQk 5. Find dx ¶ O:l for the following functions. — (a) 10 points y = x- + x — i 1- / (b) 10 . Islnx points y = \cos ( \4 2x ‘ Y Page 5 a H-I fl > I r 5 (1 flN : - çc C II c-km CI