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# 104 Review Sheet for MATH 140 at PSU

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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 22 views.

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Date Created: 02/06/15

Math 140 Calculus Final Review 1 In which year did Galileo Galilei died When was Issac Newton born Who else discovered Calculus besides Newton 2 Find limit analytically a hm 2 7 4 b hm z 5H 172 z 7 2 724 6 7 7 2 7 2 c hm x d hm z 1H2 2 7 i m72 f 7 2 2 1 7 z z 7 2x 7 10 e 139 2 7 x f mgr m 2 7 z 7 4224 sin z cos x 7 1 mnlt gt a lt7gt U Using the de nition of derivatives nd f for a we 7 i b M 7 w 7 2 c we 7 g d M 7 z3 4 Find equation of tangent line of f at z a for the following a fz z2 b fzxz727 z6 c fsin7 z 5 Find 7 for the following implicit functions a x2 zyz e 2003 b 2 y3 3ny c x735wy 0 at 30 d 4 at 91 6 The following functions satisfy the conditions for either the MVT if not Rolle s theorem nd the value of c in the conclusion of MVT Rolle s theorem afxsinx 7T27T bfxx37z 711 c f 5 7 2 z 6 722 df 2 z 6 712 1 A spherical snowball is melting at the rate of 27139 cubic inches per minute At what rate is the radius decreasing when the radius is 3 inches Hints V gm 8 A 10 foot ladder is leaning against the wall The bottom of the ladder is being pulled away horizontally at a speed of 3 feet per sec Calculate how fast the top of the ladder is falling at the instant the top of the ladder is 6 feet above the ground 9 The sum of two positive numbers is 15 what is the smallest sum of their fourth powers 10 A box with surface area 120 square feet has its length equal twice its width What dimension of this box has a maximum volume 11 Two rectangular adjacent eld share one side of their fence If the total length of fence used is only 700 feet what dimension of the eld has a maximum area 12 A factory makes cylindrical cans of volume 50007713 If they want to use the least amount of metal what should they make the diameter and height of the can If the metal for the top and bottom of the can costs half as much as the metal for the sides what should the dimensions of the can be to minimize the cost 13 14 15 16 17 18 19 Determine on which intervals the following functions are increasing or decreasing Concave up or concave down Use the 2nd Derivative Test to test all its critical numbers 1 b 10 d y 5x3 7 3x5 a y ass i z 0 Sketch the graph of the following by analysing its rst and second derivatives domain inter cepts asymptotes symmetry extremas and concavity 2 a M b M 1 6 yxew m c fzz1z2z4 Use the Fundamental Theorem of Calculus to nd the derivatives of dz c Fz tsintdt a FzOm1t3dt b FzO 1t3dt d Fz15t2dt e Fz155imsxlsds f Fx251sds Using 71 equal subintervals approximate the de nite integrals of the following by a sum in sigma notations by evaluating the right end point of each sub interval a A3x2 dz b 027x1dx c 0117x3 dz Find their limits as 71 goes to in nity Evaluate the following a 28 x i 3 dz 2 b 4 se02x5 dx c 2 coshx3 dx lny 2z1 2z1 d d d e ltz2zgt21d9 f 1z22d 1 212 003 g 2 26 10 dz h 1x3 dx 1 T 1112966196 1 72 6 dz k 0 xzema dz d lm dz Find the general solution of the following DE 2 2 a 112 b 2zy 5y c lt1z2gty lt1y2 Solve the following DE with the given initial conditions i 7 a y 7 y y2 72 b y 75y 110 100000 C y 72y i 60 y1 70

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