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fin06k - ) at the point where t = / 6. For maximum credit,...

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MAC 2311 April 24, 2006 Final Exam Prof. S. Hudson Name Show all your work and reasoning for maximum credit. Do not use a calculator, book, or any personal paper. You may ask about any ambiguous questions or for extra paper (but hand it back in). Good luck! 1) (15 pts) Compute and simplify; R 1 + 2 x dx = R sec( x ) tan( x ) dx = R 1 - 2 t 3 t 3 dt = 2) (10 pts) Find the maximum and minimum values of f ( x ) = | 6 - 4 x | on the interval [-3,3]. 1
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3) (20 pts) Compute; d dx sin( x 3 ) d dx 3 x +2 d dx cot( x ) Find dy/dx , given that x 2 + y 2 = 100 4) (10 pts) CHOOSE ONE; A) State and prove Rolle’s Theorem. B) State the definition of limit, and use it to prove that lim x 10 4 x + 50 = 90. 2
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5) (10 pts) A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see figure below or on the board). What dimensions should be used so that the enclosed area will be a maximum? [If you don’t understand this story, ask me!] 6) (10 pts) Find the slope of the tangent line to the curve, x = 2 cos( t ), y = sin( t
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Unformatted text preview: ) at the point where t = / 6. For maximum credit, use the chain rule as done in class. 3 7) (10 pts) Answer TRUE or FALSE: The sum of any two continuous functions dened on (- , + ) is also continuous. A continuous function dened on (- , + ) must have a minimum value. A rational function is continuous everywhere except at the points where the denomi-nator is zero. If f is dierentiable on the open interval ( a, b ) then it is continuous on the closed interval [ a, b ]. The function cot( x ) is continuous on the interval (-/ 4 , / 4). 8) [5pts] Compute lim x + (1 + 2 /x ) x = 9) [5pts] Find all the discontinuities of f ( x ) = csc( x ). 10) [5pts] Suppose a particle has position s ( t ) = t 3 / 3-2 t 2 + 5 [so, v ( t ) = t 2-4 t and a ( t ) = 2 t-4] for t 0. When is the particle speeding up? slowing down? Explain briey. 4...
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fin06k - ) at the point where t = / 6. For maximum credit,...

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