# Final-Math1342-Spring2020-Solutions-VAL.pdf - SOLUTIONS...

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Math 1342 Spring 2020 Final Exam Name: For pages 1-4, you need to show all your steps to get full credit! 1. (6 pts) Evaluate the integral: 2 1 ln( x ) x 2 dx 2. (6 pts) Evaluate the following improper integral or show that it diverges: 1 1 (3 x + 1) 2 dx SOLUTIONS HATE = - ¥ 1 ? - STIFF )d × u=hxdv=x-2dx = - had + Six - adx du - - Lxdx V= - x " = - hast Ii = - had - Latta - that's ' Ii :S .bz#nzdx=fiIS ! btttzu-2duu--3xti=-lbizfIly3btYdu-- 3dX 3 , I =dX 0 ¥ .Yu=4 = tht . x=bu=3bH 3 - I = - 12
3. Let R be the region bounded by the graphs of y = - x 2 + 2 x + 2 and y = x . Set up, but DO NOT EVALUATE, an integral for the volume of the solid you get by revolving the region R about: a) (5 pts) the line y = - 3. b) (5 pts) the line x = - 2. 4. (5 pts) A tank has the shape of an inverted right circular cone (axis vertical, vertex pointing downward, circular base at top), with altitude 15 feet and base radius 5 feet. It is filled to a depth of 12 feet with a liquid having a weight-density of 63 pounds per cubic foot. Set up, but DO NOT EVALUATE, the integral for the work W done in pumping all the liquid in the tank up to the top of the tank. - x2t2xt2=X XZ - X - 2=0 ( x - 2) ( xtl )=O X=2 , -1 Pts :( 2,211-1,1 ) y= -42+2*2 Washers Wrt X R=-x2t2xt2 - f- 3) = - x2t2xt5 ¥ -1 r=x - I -3 )=Xt3 £ ! T(fx72xtSKCxt35)dx ' =-3 G shells wrtx y=-x2t2xt2 r=X - f- 2) =Xt2 ¥ x h= -542 × +27=-54 × +2 y f ! 2IT(xt2)fx7xt2)dx * -2 s 15 1 ¥ , it , ft : ft - lb E ' a wsiici-63.it/IzYsy.ll5-y ) Psy - y O 5 Er ! 'T , :3 . 1%311-7415 - g) dy F- Iz
5. Given f ( x ) = x + 1 a) (5 pts) Find the third order Taylor polynomial centered at a=3, T 3 f ( x ; 3).
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