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Calculus I

by: Felicita Lockman
Felicita Lockman
GPA 3.68


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Class Notes
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This 3 page Class Notes was uploaded by Felicita Lockman on Sunday October 25, 2015. The Class Notes belongs to MATH 1241 at University of North Carolina - Charlotte taught by Staff in Fall. Since its upload, it has received 19 views. For similar materials see /class/228922/math-1241-university-of-north-carolina-charlotte in Mathematics (M) at University of North Carolina - Charlotte.


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Date Created: 10/25/15
Math 1241 Spring 2008 Second Practice Midterm March 2008 Instructor Catalin Turc You must show all your work to receive credit Important No books graphing calculators or notes are allowed Cheating may result in failure of course dont even think about it Please read each question carefully7 show all your work7 and check afterwards that you have answered all questions correctly Any crossed work will be disre garded even if correct Write one clear answer with a coherent derivation Good luck 1 Given the function fx nd a formula for f using the de nition with limits af ifzh fz 1 71 aflt gt gmwh 2 hmlizih2z71iz2zh haO h2z2h hm272hisixhisz727xh7xhiz2 haO h2z2h 73h 3 1 7 hIEtljh2z2xh 2z2 Vzhi llm haO h hao h 711m h7ih M MPHHm xh7 h lim lim MhWHH whw wm i 1 1 53 m W M 39 2 The equation of motion of a particle is s t3 7317 where s is in meters and t is in seconds Find a the velocity and acceleration as functions of t b the acceleration after 25 c the acceleration when the velocity is 0 d when is the particle moving forward a vt s t 3t2 7 3 and at it 6t b after 25 the acceleration is 12 12m52 c the velocity being equal to 0 means that we have to solve the equation 11t 0 that is 3t273 0 ltgt t71t1 0 i t 1 since that is the physical value for the time At time t 1 the acceleration is 11 6 d The particle is moving forward when the velocity is positive7 which is 3t273gt07 andwegettgt 1 3 Compute the derivatives of the following functions using the appro priate rules of differentiation 61 a g a Use the quotient rule and get y w 7 3x 7 1 7 2x 1 My b Use the quotient rule again and get y W cm 7 z 6W3 7 W C Use the product rule and get y 1 em 3 7 7 a 2 1 sin x d y z cos x d Use the quotient rule and get y 4 Compute the derivatives of the following functions using appropriate rules of differentiation and the chain rule 7r ay x6 a Use the product rule to get y 67 z e wZ For this derivative we apply the Chain rule e w2 67 7x2 72m w Finally we obtain 712 7 2 y i e 1 2x 71 b 1 y z1 l 2 Then apply the Chain rule to get 171 il 71 2 71 9 2 z1 z1 71 x71 2 2 2 z1 z12 7 717 7 z1 b First write y up 1 96 12 i 1 1711339


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