Final_exam_ _-4

Final_exam_ _-4 - Math 140 Final Examination Fall, 2002...

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Math 140 Final Examination Fall, 2002 Instructions: Answer each of the 10 numbered problems on a separate answer sheet. Each answer sheet must have your name, your TA’s name, and the problem number (=page number). Show all your work for each problem clearly on the answer sheet for that problem. You must show enough written work to justify your answers. NO CALCULATORS 1. (8 points each) In each of the following, determine whether the limit exists as a real number, as or -∞ , or fails to exist. If the limit exists, evaluate it. a) lim x →∞ sin 5 x 3 x b) lim y 1 - p 1 - y 2 y - 1 c) lim x 0 5 e 3 x - 5 2 x 2. (8 points each) Compute the following derivatives (you do NOT need to simplify your answers): a) d dx ± xe ( x 2 ) ² b) d dt ³ Z t 2 4 t x ln(1 + x ) dx ! c) d dt (ln(tan t + sec t )) 3. (20 points) An isosceles triangle has base 6 and height 10. Find the maximum possible area A of a rectangle that can be placed inside the triangle with one side on the base of the triangle. Explain why your answer gives the maximum area as opposed to the
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Final_exam_ _-4 - Math 140 Final Examination Fall, 2002...

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