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# CALCULUS I MATH 2144

OK State

GPA 4.0

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This 0 page Class Notes was uploaded by Hector Hudson III on Sunday November 1, 2015. The Class Notes belongs to MATH 2144 at Oklahoma State University taught by Mahdi Asgari in Fall. Since its upload, it has received 45 views. For similar materials see /class/232783/math-2144-oklahoma-state-university in Mathematics (M) at Oklahoma State University.

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Date Created: 11/01/15

Review for Exam 3 Math 2144 Sec 003 amp 010 Fall 2008 110 pts each Find the following integrals Use C for the constant a 72x3 352 5 dz b cosz 7 sec2m dz 1 c 7 d lt gt T i z 15 2 7 7 d 5 m de 2 Find fz if f z 75x4 6x and f71 1 3 Evaluate the following de nite integral Simplify your answer as much as possible 7r3 cosz dm 7r6 4 Find the derivative of 9 if gm V1x2dm 3 5 Use a limit of Riemann sums with right endpoints to evaluate the following de nite integral You may use the formula 1 2 3 1 n 7 1 n ME Show your steps 5 3m dm 0 6 6 Approximate the de nite integral dz with n 2 subintervals using the m 1 follwoing methods In each case simplifif yo r answer to a single fraction Make sure you check your calculations carefully a The midpoint rule b The right endpoint rule 7 Find the area of the region enclosed by y z 7 1 and y2 2x 1 Simplify your answer as much as possible 8 If fz is de ned as follows7 nd its derivative f z You need not simplify your answer 3 m 1 m m2 2 sint dt 9 Find the volume of the solid obtained by rotating the region bounded by y z and y E a about the z axis Simplify your answer as much as possible b about the y axis Simplify your answer as much as possible Review for Exam 2 Math 2144 Sec 003 amp 010 Fall 2008 1 A rectangular storage container is to have a volume of 60 ms The length of its base is twice the width Material for the base costs 4 per square meter and the material for the sides and the top cost 6 per square meter Find the dimensions of the cheapest such container 2 The curve y V m2 4m has two slant asymptotes Find both of them 3 For the following function7 nd the domain7 all intercepts if any7 equations of all asymptotes if any7 intervals of increasedecrease7 points at which 1 has a maxi mum minimum7 intervals of concave upconcave down7 and points of in ections if any Then sketch its graph carefully incorporating all the above features 72m5 re 3 4 Find the derivatives of each of the following function a x2mz71z72 wgte esz7va2 c sinsinz 1 7 d 5 Use linear approximations to estimate V998 6 Two cars start moving from the same point One travels south at 60 mih and the other travels west at 25 mih At what rate is the distance between the cars increasing two hours later Simplify your answer as much as possible 7 Find D21sin2m 8 Calculate the following limit 2 3 hm s1n maO x 9 Find the points on the graph of m2 y22 2z2 7 yz called a lemniscate where the tangent is horizontal Don t spend time trying to sketch the graph You do not need it for your solution If you are curious7 it looks like an 8 on its side For each such point7 your answer should be the exact coordinates of the point7 simpli ed as much as possible Review for Exam 1 Math 2144 Sec 003 amp 010 Fall 2008 1 Let x7x if m lt 0 m 37m if 0 mlt3 x 7 32 if m 2 3 Evaluate each limit7 if it exists a lim170 1 b limwm 1W 0 hmmaO 1 d limmhg ag 8 hmmai r 1 f limes 1W 2 Find the exact value of m3 7 8 312 2 7 439 If the limit does not exist7 then enter7 gt07 700 or DNE as appropriate 3 Find the following limit You answer should be a numloer7 oo7 foo or DNE lim sec5z ma77r1O 4 Find an equation of the tangent line to the curve of y 2x2 1 at 17 3 5 Find the exact value of the following limit7 if it exists If the limit does not exist7 then enter oo7 foo or DNE as appropriate i V6772 lim zaz Bizil 6 ls there a number that is exactly 1 more than its cube Explain 7 Find the constants A and B such that the following function is continuous every Where Am2 1 1 if m g 1 Bx 7 A if 1 lt m lt 2 Bxg if m 2 2 Review for Final Math 2144 Sec 003 amp 010 Fall 2008 1 Find the following integral Use C for the constant x2 xsx31dx 2 Consider the function x on the interval 1 5 2 x 32 a Find the exact value of the average fave of x on 1 5 b Find all numbers 0 in 1 5 that satisfy the Mean Value Theorem for lntegrals ie 106 fave 3 Find the following limit Hint 1 7 cos2x sin2x h 17cosx x70 sinx 4 Find the area of the region bounded by y x2 and x yz Simplify your answer as much as possible 5 If x is de ned as follows then nd its derivative f x 35 x1t2dt 3 x2 x 7 5 x 7 2 39 7 An aquarium 10m long 5m wide and 2m deep is full of water How many joules of work is needed to empty the aquarium by pumping all of the water to the top The density of water is 1000kgm3 and g 98m52 Simplify your answer as much as possible 6 Find the equations of all the asymptoes if any of y 2 dx with n 3 subintervals using the 0 follwoing methods In each case simplify your answer to a single fraction Make sure you check your calculations carefully a The Midpoint Rule b10 pts The Trapezoidal Rule 8 Approximate the de nite integral 9 Find the volume of the solid obtained by rotating the region bounded by y x2 and y x3 a around the x axis using washer method Simplify your answer as much as possible b about the y axis using shell method Simplify your answer as much as possible

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