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# Calculus II MATH 132

UMass

GPA 3.55

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This 2 page Class Notes was uploaded by Reuben Hudson DDS on Friday October 30, 2015. The Class Notes belongs to MATH 132 at University of Massachusetts taught by Staff in Fall. Since its upload, it has received 17 views. For similar materials see /class/232223/math-132-university-of-massachusetts in Mathematics (M) at University of Massachusetts.

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Date Created: 10/30/15

lllllllllll llllsllllllll SEE 1 1 An object is thrown from the top of a 126 foot tall building with an initial velocity of 80 ftsec in the horizontal x direction with an initial velocity of 64 ftsec in the vertical y direction a Sketch a graph of the path of the object b Find the parametric equations that describe the velocity at any time t c Find the parametric equations that describe the position at any time t d Find the maximum height that the object attains e Find the speed of the object at its maximum height f Find when the object passes the top of the building on its way down g Find the distance of the object from the building at the time found in f h Find the displacement of the object at the time found in e i Find the total distance traveled at time found in e 139 Find the speed with which the object strikes the ground k Find the distance from the building of the object when it strikes the ground 1 Find the total distance that the object travels Show both the integral and the value mFind the displacement of the object when it is on the ground 2 Determine if each of the following sequences converge or diverge Explain your answer This means If the sequence converges find the limit If the sequence diverges show the limit does not exist n5 5n3 10TE a tan 4n5 7n4 l b 1n n3 n 10 lOln2 3nl 3 2 0 cos 4n 751n 10TE 3n 1 3 Find a jln xdx b Djxe X dx 4 Use integrations by parts to find I ex cos x dx Calculators should not be used 4n3n 5 Show that 3 I10 2n 5 diverges Explain your answer l 6 Find a geometric ser1es whose sum is 1 when le ltl X 7 Consider the 4 leafrose r f9 sin 29 polar coordinates a Sketch the graph of f when 0 S 9 S TE If you use calculator be sure to include the size of the window that you are using b Find the area of one of the leafs 8 This problem is in polar coordinates The region R bounded by rcsc9for SQS 4 2 TE rsec9for09 S r for OSGSE sm 9 cos 9 2 a Sketch R b Find the area of R 9 Find an equation of the line tangent to the curve described by the parametric 7 t equations X e at e4 J2 yt cos t s1nt 10 Find l exsin X dX X tan t 11 If the curve C is described by t nd an equation of the line tangent to C y sec atl J5

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