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# Intro CalcBusiness Applicatio MATH 108

Mason

GPA 3.85

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This 2 page Class Notes was uploaded by Michale Kuhlman on Monday September 28, 2015. The Class Notes belongs to MATH 108 at George Mason University taught by Staff in Fall. Since its upload, it has received 24 views. For similar materials see /class/215008/math-108-george-mason-university in Mathematics (M) at George Mason University.

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Date Created: 09/28/15

MATH 108 Introductory Calculus With Business Applications Review sheet for the nal exam 1 Determine where l2x 3 is continuous and where it is differentiable Sketch the graph y 2 Determine the constants a and I such that the following function is differ entiable 7 x3x1 ifoZ x7 1195 ifoZ 3 Differentiate the following functions 1106 ergx1 f2x 53 5 1 f3x ln9c3 95 1 mac In W f5x ln9c3 95 1 f6x lnx3 lnx 1 f7x ln9c3 lnx 1 4 Find and classify all the critical points of 2x3 15952 3695 1 Determine where is increasing and where decreasing Find the points of in ection and determine where is concave up and where concave down Use this info to sketch the graph y 5 A jar lled with sweet jam has 1000 germs of a particular type These germs are multiplying like crazy and their number is quadrupling each hour After how long have their number reached one billion 6 Solve the following equation 311 7 32 2 What is the derivative of the LHS 3 1 32 Does 3 1 32 have a critical point 7 The speed vt of a car at a given time t is given by vt 2 g 3 How far has the car gone during the rst 10 seconds If the car starts 100 meters from a tree and drives directly away from the tree how far is the car from the tree after 20 seconds Assume all units are meters seconds and the speed is meters per seconds 8 Find the following integrals i e antiderivatives x5 dag d de e bdx x where a and b are some constants 9 Find the area bounded by x2 7 1195 10 and the xaxis 10 Let 2lnxlnx1lnx71i Solve the equation 0 Show that A always has a solution in some positive as for every real constant A 11 Compute the derivatives of the following functions 3 x3 lnx3 31m 12 Compute the derivatives of the following functions vi imMMSWV 13 Compute the derivative of the following functions fmm Here f and g are arbitrary functions 14 Let Px f1 Show that Pm m m PW f195 f295 In general show that if Px then M M Pm hm mn 15 Use the above formula for the general n to compute the derivative of the following function x z 1z Mac 3W 44z 55z 66x 7 16 Suppose a principal of P 3000 dollars is invested at an annual interest of r 17 percent H If the interest is compounded monthly what is the balance after 5 years P If the interest is compounded continuously what is the balance after 5 years US 1 How long must you wait if you want the balance to be double that of the original principal if the interest is compounded once a month tb How long must you wait if you want the balance to be double that of the original principal if the interest is compounded continuously

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