Practice Final (v2) Fall 2010

# Practice Final (v2) Fall 2010 - MATH 3 FINAL(Version 2...

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Unformatted text preview: MATH 3 ' FINAL (Version 2) 12/08/2010 Instructor: N andini Bhattacharya Use of books, notes and graphing utilities is not permitted in this exam. Show all your work to get partial credit. Good luck! Your Name ------------------------------------------ -- Your TA --------- -+ ----------------------- -—_ ------ --- Max Your score r Max Your score Problem 1: 15 I Problem 11: 15 Problem 2: 15 ‘ Problem 12: 15 Problem 3: \25 Problem 13: 10' Problem 4: 10 Problem 14 (EC): 15 Problem 5: 25 Problem 6: 15 Problem 7: 20 Problem 8: 10 Problem 9: ' 15 Problem 10: 10 TOTAL: 1. (15 points) Consider the function y z —ZCos(2x+7c)+1. Find the following: (a) (1 point) The amplitude of f. (b) (2 points) The period of f. (c) (2 points) The phase shift of f. _ (d) (6 points) The graph of f labeling all points. e) (4 points) Now graph y = —2sec(2x+ n)+1 into the same coordinate system above. 2. (15 points) Let f(x) = x + 3, and g(x) = x2 + 4x -—1 . a) Find the minimum value of go f. b) Find the minimum value of f o g. c) Are the results in parts (a) and (b) the same? 3. (25 points) Find all solutions for the following functions: a) 33x+2 = 5 b) lnx = ln(2x —-1)-— ln(x— 2) 0) 251119 + «B = 0, all 9 d) 200529 + \$111.29 =0 e) 4c0822x—4cos2x+1=0 osx \$27: 4. (10 points) Give the exact values (not calculator approximations) of the following : f I _1_—2 a) sm( 2) b) sin“1[sin(-7r )] c) tan[sin'l[—%D by using (and drawing) the appropriate triangles d) cot[cos'1(—%) + cos—1(0) + tan—Kg) 5. (25 points) Prove the following identities: 2c032x—1 _—— = cotx — tanx smxcosx d) sin(2x) = (tan x)(1 + cos 2x) e) sinx + cosx = ﬁcosbc - E) 6. (15 points) A promissory note will pay \$40, 000 at maturity 15 years from now. How much should you pay for the note now if the note gains value at a rate of 7% compounded continuously? 7. (20 points) a) A regular pentagon is inscribed in a circle of radius 2ft. Find the area and the perimeter of the pentagon. Hint: to ﬁnd the perimeter, ﬁrst ﬁnd the length of a side using the law of cosines. 8) (10 points) Let f(x) = tan(x+ 13—). Graph one period of this function specifying the intercepts and asymptotes: 9. (15 points) The point P lies in the ﬁrst quadrant on the graph of the line )7 = 5 — 3x. From the point P, perpendiculars are drawn to both x-axis and the y-axis. What is the largest possible area for the rectangle thus formed? 7......“me 1 10) (10 points) Give domain, range and a good sketch of the graph . . 7: of the Inverse funot1on y = tan"‘(x) + Z 11. (15 points) Solve the following triangle: <A = 41°, _<B = 33", 0221 ft 2x2—3x—2 x2—3x—4 12. (15 points) For the rational function do the following: a) Find all x-intercepts (if any) b) Find all y—intercept. c) Find all vertical asymptotes. (1) Find the horizontal asymptote. 6) Sketch the graph (label the axes, asymptotes and all intercepts): 13. (10 points) Evaluate each expression: 21) Given sect = —2, andtant > 0, ﬁnd cos(t) b) Given cos(9) = g , 00 < 9 < 900 ,ﬁnd (308(90O —6) e) csc(—120°) 14. (15 points) Extra Credit 3n a) Compute the ﬁrst four terms of the sequence an = +1 :1 b) Rewrite the following sum using 2 (sigma) notation: (:1) Find a fraction equivalent of .545454545454545454. . ' a ...
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Practice Final (v2) Fall 2010 - MATH 3 FINAL(Version 2...

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