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# CALCULUS I ENGR MTH 151

UM

GPA 3.82

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This 4 page Class Notes was uploaded by Lela Feeney on Thursday September 17, 2015. The Class Notes belongs to MTH 151 at University of Miami taught by A. Bystrik in Fall. Since its upload, it has received 4 views. For similar materials see /class/205711/mth-151-university-of-miami in Mathematics (M) at University of Miami.

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Date Created: 09/17/15

UM Calculus I Midterm 3 Review Lecturer Dr Bystrik bystrikmathmiamiedu The problems herein are representative of the pool of the problems you might see on the third midterm Not every problem type Will be present but every one of the problem types discussed in this review might be present The actual midterm Will be 1 N 9 composed of 4 to 6 problems with subproblems for the total of 40 points 20 of your grade Use the properties of de nite integral to evaluate a Area under the curve y 4x l on 02 b Area restricted by Ox and the curve y 4x l on 2 2 Evaluate the antiderivative a 17 5 3Jf 3 ujw f mma c de d Icotxdx e ex 7sinxdx f Icosxdx Antiderivatives and de nite integrals Evaluate using the substitution a J1de 72 dx 539 Iamwa 01 J e3xdx 0 1 Jxzexgdx 0 2 5 D J sin nxdx 1nx dx 4 For the following problem you may either to solve for the constants or use the net change theorem FTC Part 1 We use the usual notation for a linear motion problem Given the acceleration at 0 2t2 and the initial conditions for the position and the velocity yl 10 v1 4 nd a vt b v2 6 N d y2 e vmmge with respect to time t on 1 2 5 fx Jntdt a Find the derivative of this nonelementary function using FTC b Find the critical points c Find the xcoordinates of the points at which the tangent line is horizontal d Find the equation of the line tangent to y fx at P 1 0 6 Compute the average value of a x cos 27m on an interval a 01 b 025075 1221 7 The integrals ofthe type J xipdx p gt 0 1 b a Find the area under the curvey 1 on 1 b for b 2 1 Hint Ab J 1 dx x 1 x b FindA1 A4 A16 c Find ling1 d Nowanswerthe questions a b c fory andy J 8 Find the mean value of fx 1 on 1 b x 9 Use any method to evaluate a 27 J sinzwxdx o b fJRz xzdx 0 10 What is the average value of a cosine function over its period starting anywhere UM Calculus I Midterm 1 Review Lecturer Dr Bystrik bystrik mathmiamiedu The problems herein are representative of the pool of the problems you might see on the rst midterm Not every problem type will be present but every one of the problem types discussed in this review might be present The actual midterm will be composed of 4 to 6 problems with subrproblems for 40 points total 20 of your grade 1 Check all that applies Transcendental Rational 213x3 2 Refer to the property of limits for composition of functions lim f o 9W f1im 9W rma as a Assuming the corresponding limits exist7 check the correct box to continue the general statement The property holds true always if f is continuous at lilnx magac only if both f and g are continuous at a 3 Evaluate the following limits a lim tanac mag 25 7 5 b hm L 1H0 ac ac llm 7 zgt0 s1n 235 f m 50000012008 413 e 02x acgt00 000004r2009 00000000001290 01 g lim 2amp1 35 ssoe lnac h li zlgonJr cme 75 139 s1 x2 e 101 25

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