217-zhu-07spfin - MATH 217 FINAL(SPRING 2007 Name Section...

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Unformatted text preview: MATH 217: FINAL (SPRING 2007) Name: ____________________________________ Section: ___________ TA: __________________ Score: Problem 1 ____________________________ Problem 2 _____________ ,- ______________ Problem 3 ____________________________ Problem 4 ____________________________ Problem 5.___. ________________________ Problem 6 ____________________________ Problem 7._l____l ____________________ L Problem 8 ____________________________ Total: ___________________________ Instruction: Show all work. No work = no credit, even if you have a _ correct answer. References and calculator are not allowed. Problem 1 15 points): Compute the following: (a) 3%(COS_1(€$)) (b) f Watt 7T (C) E COSCL‘ d1. 0 2+sin w Problem 2 (20 points): Suppose that the distance between Tom’s two eyes A and B is 1 inch. If he looks at an object C such that the line AC and BC’ form 105° and 45° angles respectively with the segment AB, as illustrated in the following figure, then (a) What is the distance from C to A? ( Hint: Law of Sines ) C (b) What is the distance from C to B? ( Hint: You don’t have to know sin 1050 if you apply Law of Cosines to 1B : 45°. ) Problem 3 (10 points): Use the dot product to find the angle 9 between the vectors if: (3,1) and b = (—4,2), where 0 g (9 3 7r. Problem 4 (15 points): Evaluate the following expressions of complex num— bers, where 7) = \/—1 is the imaginary unit: (a) 1+3i 1—1 (b) li3(1 ~01 (c) (1 + 2')8 ( Hint: De Moivre’s Theorem ) Problem 5 (10 points): Jerry bought 10 candies for $1. There were two kinds of candies; the, coffee candy is 7 cents each and the berry candy is 12 cents each. How many of each kind of candies did Jerry buy? Problem 6 (10 points): Prove that Ina: = 0(fi) as 30 —> +00, '1.e. lnsc is of smaller order than fl as x ——> +00. Problem 7 (20 points): Consider the function f (x) = 332(53 — 1), where —00 < x < +00. (a) Using the local picture of real polynomials nearby real zeros, sketch the graph of f (x) (The graph should at least display the zeros and signs of f (cc) correctly.) (b) Find all local extrema of f. Problem 8 (10 points): The region R in the first quadrant is bounded by the curves y = as and y = :03, Where 0 g :1: S 1. (a) Find the area of the region. (b) If the region is revolved about the x-axis to generate a solid, what is the volume of the solid? ( Hint: washer’s method ) 10 ...
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