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# Calculus and Analytic Geometry MATH 221

UW

GPA 3.8

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This 2 page Class Notes was uploaded by Zechariah Hilpert on Thursday September 17, 2015. The Class Notes belongs to MATH 221 at University of Wisconsin - Madison taught by Qian You in Fall. Since its upload, it has received 16 views. For similar materials see /class/205271/math-221-university-of-wisconsin-madison in Mathematics (M) at University of Wisconsin - Madison.

## Reviews for Calculus and Analytic Geometry

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Date Created: 09/17/15

Math 221 Review Answers 1 Calculate the derivative of the following functions 12 cos31 91 arcsin 6 My 2121 1 11 17 arctan ln 12 W 605w 31 I 3 3 ln 1 2 Find the nth order derivative of the following functions 25 3 7 ms 4 1 91 12I 1 2x hz e 1z 3 Find for the following implicitly de ned functions 2 2 a 2 1 w b y21em 3y7 n coszsinycosysinz 1 4 An isosceles triangle is changing its shape the length of the base the nonequal side is xed at 2 inches but the angle 9t between the two equal sides changes If the area At changes at a constant rate of 1 inch2 per second how fast is 9t changing when 9 600 5 Where does the function V2 7 312 have horizontal tangents Vertical tangents 6 What is the statement of the mean value theorem 7 What is the statement of the intermediate value theorem 8 What is one area where we use the intermediate value theorem ie Give an example of a situation where we use it 9 Sketch the graphs of the following functions 13 212 z 2 1 91 7 71 12 cosz Mr 7 1 cos I ln 12 I and z gt 0 6 11 7 1 1 kltgt cos 6 1 z ln 12 You may use that 1 0 only when I m 0703 ex ln 3 10 What is the largest sinz siny can be if z y g 11 A company wishes to sell gadgets If the company decides to make 1 gadgets each gadget will cost 1 4 dollars to make The company can sell the gadgets for 40 dollars apiece If the company wishes to maximize their pro ts how many gadgets should they make 12 Find the following limits 2x A hm EH00 e275 I4 B 1 2x31 1m 7 EHO e275 I4 z231 C 3201 V D 7 139 feu 7 xirgom 1 71 E lim 6 5 0H0 270 2 lnzln12 F 111330 11115 z 12 G l 1131 1 lnz10 H z 12 l39 0631010 I lnz10 13 A population of rabbits will be tripled three months from today How long will it take for the number of rabbits to be ten times what it is today If there are 800 rabbits one month from now how many rabbits are there now 14 If there was 15 grams of a radioactive substance yesterday and there will be 12 grams tomorrow how many grams are there today What is the substances halflife

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