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# CALC OF ONE VAR I MTHSC 106

Clemson

GPA 3.76

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This 2 page Class Notes was uploaded by Jazmyn Braun on Saturday September 26, 2015. The Class Notes belongs to MTHSC 106 at Clemson University taught by Allen Guest in Fall. Since its upload, it has received 83 views. For similar materials see /class/214281/mthsc-106-clemson-university in Mathematics (M) at Clemson University.

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Date Created: 09/26/15

Mthsc 106 Fall 2010 Final Exam Review 1 Use analytical methods to evaluate each limit If a limit does not exist explain why Show all work for full credit 3 3 7 7 3 3 a lim L b lim QC 4 c lim M257 0 x H 2x 5x 6 H1 2x 5 3 1 e2x d 11m xln l e 11m7 H x H0 lnx 1 2 Find the derivative of each function Z x a gx 7 b fx mug c y eln4 d ht 517csct1 I 2 e y sece 2 f hx tan sine3x g y xms m 3 Evaluate the following integrals Clearly show all work including any variable substitutions 3 2 x a 77 csc2x 7dx b dx Id x2 Ix43x2 lnx k c Isms xcosx dx d Jde ka constant 6 4 Find the equation of the line tangent to the graph at the indicated value of x 7r fx tan2x 1 x E 5 Using the limit de nition of the derivative find the derivative of f x 2x2 7 9 6 A water tank has the shape of an inverted right circular cone with a base radius of 5 feet and a height of 20 feet A valve at the bottom of the tank is opened and water flows out at a constant rate of 2 fl3 min At what rate is water level falling at the instant the water in the tank is 8 feet deep Your solution should contain a welllabeled picture with defined variables an equation that describes the situation and all calculus and algebra needed to determine the answer Your final answer should be stated as a complete sentence with proper units Note The volume of a right circular cone is V rzh 7 Because of its larger mass acceleration due to gravity on the planet Jupiter is approximately 26 m sec2 take downward to be the negative direction in your work below a A stone dropped from a height of 500 meters Using calculus techniques determine how long it will remain aloft Round your final answer to the nearest hundredth of a second b What is the speed of the stone nearest hundredth upon impact with the ground 8 Afarmer has 200 feet offencing with which to construct three sides ofarectangular pen the fourth side ofwhich will be an existing wall ofalar e bam What dimensions will maximize the area ofthe pen Your solution should contain a welllabeled picture with defined variables an equation that describes the situation and all calculus and algebra needed to determine the answer Your final answer should be stated as a complete sentence with proper units 9 Let fbe afunction continuous on ino r no The graph ofthe derivative offis shownbelow Use it to answer the questions that follow a For what values of does fhave a local minimum Justify you answer b Forwhat values of does fhave alocal maximum Justify you answer c on what intervals is fconcave up d on what intervals is fconcave down Given that o 1 sketch apossible graph off showing any inflection points 10 Does there existaneverywhere continuous differentiable function fsuch that oo and l4where f39x 3 for all x 5 01 Explain Hint rMean Value Theorem 11 Consider the parametric curve defined by x sin y 17 1 Find the equation ofthe quot L L 39 L h i I 0

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