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# Calculus I MAC 2311

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This 1 page Class Notes was uploaded by Duane Bayer on Wednesday September 23, 2015. The Class Notes belongs to MAC 2311 at University of South Florida taught by Arthur Danielyan in Fall. Since its upload, it has received 12 views. For similar materials see /class/212640/mac-2311-university-of-south-florida in Calculus and Pre Calculus at University of South Florida.

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Date Created: 09/23/15

15 16 17 18 19 20 22 23 24 25 26 a State Rolle s Theorem and the Mean Value Theorem MVT b Find each value of c that satisfies Rolle s Theorem on the following intervals If not possible state WhY 1 fr sinm cos2 a on 7r 27139 2 f 2 m23 on 11 3 fa tans on 07r C Use Rolle s Theorem to show that f m 31 cosx 1 has exactly one real root 1 Find each value of c implied by the MVT for f 33 5 011 0 4l 8 Find the value of c implied by the MVT for f a him on 1 e f Use Theorem 28 Chapter 4sec 23 to verify that sin2 1 cos2 x 1 Hint let f at sin2 1 cos2 1 If f 0 4 and f g 2 for 0 S a lt 6 nd the largest possible value of f 2 x ata1 617 3333 2 at a 2 Use it to approximate 38228 Find the linearization of f Find the linearization of f a If f m 2 m2 293 3 nd the actual change in f when 1 changes from 0 to 015 b Find the approximate change in f 3 using differentials A Window has the shape of a square topped by a semicircle The base of the window is measured to be 40 inches in length with a possible error in meaSurement of i02 in Use differentials to estimate the maximum error possible in computing the area of the window What is the relative and percentage error The area of a right triangle with hypotenuse z is calculated using the formula 1 93251n20 where 9 is one of the acute angles Use differentials to approxrmate the error 1n 4 calculating A if a 4 cmexactly A and 6 is measured to be with a possible error of 2004 radians The monthly pro t from the sale of as units of a product is given by the formula 2 m P 1 2 10 a Use differentials to approximate the change in pro t when sales decreasa from 100 to 98 units What 18 the percentage change in pro t b Find the production level that will maximize pro t What is the maximum pro t 60x 1800 0 S a g 500 Suppose that f it has horizontal tangent lines at a 2 a 1 and a 5 If f quot37 gt 0 on intervals oo0 and 2 00 and f lt 0 on the interval 02 find the m values at which f has relative extrema Assume that f and f are continuous on oooo The stock in a particular company varies so that its value at time t in years is given by V 2 20 000 t t2 81 20 True or false a If f is increasing on an interval I then f must be concave up on I b If f m g c for all 13 then f 9 39Find its maximum value from t 0 to t 10 years Find the intervals on which fr m232r 5 is concave upward and downwards and nd 2055 10 quot w Then sketch the graph of f each in ection point Note that f 51

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