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# Calculus With Analytic Geometry I MATH 140

Penn State

GPA 3.88

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This 0 page Class Notes was uploaded by Elaina Osinski on Sunday November 1, 2015. The Class Notes belongs to MATH 140 at Pennsylvania State University taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/233010/math-140-pennsylvania-state-university in Mathematics (M) at Pennsylvania State University.

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Date Created: 11/01/15

1 2 U 4 L11 0 9 9 Math 140 Calculus Final Review In which year did Galileo Galilei died When was Issac Newton born Who else discovered Calculus besides Newton Find limit analytically 2 7 4 ltagt ltbgt x6 7 7 2 7 2 c lim d lim L 1H2 2 7 i m7tZ 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 m gt av lt7gt Using the de nition of derivatives nd f for n7i owm7ww2 cwm7 n7 Find equation of tangent line of f at z a for the following a fx z2 b f z727 z6 c fx sinx7 z 37 Find 7 for the following implicit functions b 962 23 396211 4 a x2 zyz e 2003 c z i 35 0 at 30 at 91 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 bf96 963 967 96 E 471 df96 9627 96 E 472 a f sinx7 z E 7T27T C f96 5 i 9627 96 6 22 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 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 The sum of two positive numbers is 15 what is the smallest sum of their fourth powers A box with surface area 120 square feet has its length equal twice its width What dimension of this box has a maximum volume 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 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 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 a gauge b f c yxew d y5x373x5 14 Sketch the graph of the following by analysing its rst and second derivatives domain inter cepts asymptotes symmetry extremas and concavity 2 a f96 7 b f96 7 m3 c We ltz1gtltz2gtltz4gt 7 5 i 1 6 m 15 Use the Fundamental Theorem of Calculus to nd the derivatives of 1 V5 a Fz 1t3dt b Fz 1t3dt c Fz tsintdt 0 0 m 1 551nm m2 d Fz etzdt e Fz sx1sds f Fz sxl5 d5 m 1 3 16 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 3 2 1 az2zdz b7z1dz c17x3 dz 1 O 0 Find their limits as 71 goes to in nity 17 Evaluate the following a 8 lt95 7 d c b x4se02z5 dz c z2003h3 Ch lny 2z1 2z1 d d d e ltz2zgt21d f M17629 d1 1 212 cos x d d d g 9612 2696 10 95 h 1 963 95 1 v11 sin2 95 96 g 5 l x dz k xzema dz d 7 dz x2 61 0 z lnx 18 Find the general solution of the following DE 22 2 2 a y W b Hm50 c 1y1y 19 Solve the following DE with the given initial conditions pi a y 7 y WP b y 75y 110 100000 C y 72y i 60 y1 70

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