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# Analytic Geometry and Calculus 1 MATH 1300

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This 4 page Class Notes was uploaded by Cydney Conroy on Thursday October 29, 2015. The Class Notes belongs to MATH 1300 at University of Colorado at Boulder taught by Joshua Wiscons in Fall. Since its upload, it has received 9 views. For similar materials see /class/231822/math-1300-university-of-colorado-at-boulder in Mathematics (M) at University of Colorado at Boulder.

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Date Created: 10/29/15

Math 1300 Fall 2005 Review Sheet for Final Exam 1 Evaluate the following de nite and inde nite integrals 2 3z5 7z2 z a dz 1 z b tan2 z dz og 4a 2 g 4 d 1 J dz e z4z5 7 232 dz M4 f tanzdz 0 g z5l 7 z25 dz 2 e in z2 h T dz 2 2 i 2zex dz 0 j4z3 l cosz4 z dz 4 z 1 1W 4 2 Sglve the following initial value problems w 7 iww b 3z 172 yl2 3 Find the exact area under the curve z 7 1 over the interval 13 using Riemann sums With righthand endpoints ie7 z zk a kAz You may nd the follWing formulae useful n n nnl ln7 ZkT k1 k1 2 4 Evaluate the integral dz7 given that 72 fzz2 zgt0 z zSO 5 De ne Fz by Fz 6 dt 0 a Use Part 2 of the Fundamental Theorem of Calculus to nd Fz b Check the result in part a by rst integrating and then differentiating 6 Find the area of the region enclosed by the curves y z2 and y 7 Find the area of the region enclosed by the curves y z7 y 4z7 and y 2 7 z 8 Find the volume of the solids that result When the region enclosed by the curves is revolved about a the zaxis b the y axis 9 Set up but DO NOT EVALUATE integrals that express the volume of the solids that result When the region enclosed by the curves is revolved about a the zaxis b the y axis Multiple Choice and TrueFalse questions d 10 Find i if 13y4 I7 dz A B y 2y4 c 715 31 D 715 7 312w E 0 ll Than 6173 Agto Bw 07w Dgt1 E71 12 The function 714 7 612 is concave up on mcmaw mewaw Pw4 ammmm mew 13 The function 3sin12 has an absolute minimum of A75 373 00 D7 E7 14 Express the number 60 as the sum of two nonnegative numbers Whose product is as large as possible A 555 B 1050 C 30 30 D 159 None of the above 15 True or false Given 12 7 9 on 73 3 the value c that satis es the conclusion of Rollels Theorem is c TRUE FALSE 16 True or false Given 13 on 02 the value c that satis es the conclusion of the Mean Value Theorem is c l TRUE FALSE Math 1300 Fall 2005 Review Sheet for Midterm Exam 3 1 Use linear approximation to nd sin47 2 Use an appropriate local linear approximation to estimate 48 3 Assume the earth is a perfect sphere and that the radius of the earth at the equator is 3960 miles or 20908800 feet Imagine that a string is wrapped tightly around the earth at the equator Then imagine that the string is lengthened by an amount that allows it to be strung all the way around the earth at the equator on short poles that are feet above the ground feet is a little less than of a foot or about 4 inches Use differentials to approximate the increase in the length of the string 4 Find for the following functions some of which may be de ned implicitly a y lnsinz 13 b y 5sinrwg c y tan 1ln I WM 5 Evaluate the following limits 39 Te 14 T a 11m 4 716273 574g1101 b limggnlr00 11 E C limx7oltgt 7 e214 d limgcnlr00 11 e limgcnir00 1 ln a mom i am g lim nmz sin I1 mmwm 6 Given 13 1212 3 t 7 213712 352 WWW ww 1W f I nd a z and y intercepts b vertical and horizontal asymptotoes c critical points classify each as a relative maximum relative minimum or neither d intervals where f is increasing and decreasing e in ection points f intervals where f is concave up and concave down g Sketch the curve 7 Same as 6 given I4 7 4x2 71 413 7 81 f z 1212 7 8 8 What is the length of the shortest line segment lying wholly in the rst quadrant tangent to the graph of y i and with its endpoints on the coordinate axes 9 A closed cylindrical can is made using 2 sq ft of material for the sides top and bottom What height and radius would maximize the volume of the can 10 Let z521 1 1 Use the Intermediate Value Theorem to show that the equation 0 has at least one solution on the interval 170 2 Use the Mean Value Theorem to show that there is exactly one solution to the equation 0 on the interval 170 11 Let 12 on the interval a7b for a lt 12 Which of the following values of c satisfy the conclusion of the Mean Value Theorem for f 7a2b2 2 251227a2 ab 3i 7 C 2 4lcbia 12 Use the Mean Value Theorem to prove Rolle7s Theoreml 13 Suppose Harold and Kumar race each other to White Castle and arrive at the same time Use the MVT to show that there was at least one moment when they had the same velocity

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