Practice Final Fall 2010

# Practice Final Fall 2010 - MATH 3 FINAL Instructor N andini...

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Unformatted text preview: MATH 3 FINAL 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 --4 --------------------------------------- --_I Max Your Score ' Max Your score Problem 1: 15 Problem 11: ' 15- Problem 2: 15 I ' Problem 12'": 15 Problem 3: 25 I I Problem 13: 10 Problem 4: x 10 3 Problem 14 (EC): 15 Problem 5: 25 Problem 6: 15 Problem 7: 20 Problem 8: 10 .l Problem 9: 15 Problem 10: ' 10 TOTAL: 1. (15 points) Consider the function y = —2sin(2x + 2:)+ 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 = —2osc(2x+77:)+l into the same coordinate system above. 2. (15 points) Lerf(x)=x~3,and g(x)=x2-—4x+1. 21) Find the minimum value of go f. b) Find the minimum value of f o g. 0) Are the results in parts (a) and (b) the same? ' WWWﬂmm.“.__...__-._;.%__;.;._;;..;._..._..[email protected]_ummmwmw. - 3. (25 points) Find all solutions for the following functions: a) 23H 2 5 b) 1n(x+1)=ln(3x+l)—lnx 0) 231119 +1 2 0, all 9 d) 23in29 + sin29 = 0 e) 4cos'22x—40032x+1=0OSXSZE 4. (10 points) Give the exact valuos (not calculator approximations) of 7 the following : f a) cos'l(—72) b) cos‘_l[cos( —7r )1 c) SCC(arCtan§) by using (and drawing) the appropriate triangles «E d) cot[cos"(«-—:-) + cos"(0) + tan—T?) 5. (25 points) Prove the following identities: tanx—cotx - — =1 — 200\$ch tanx+ cotx d) sin(2x) =(tanx)(1+ cos 2x) e) sinx + cpsx = ﬁcosﬁr — g) 6. (15 points) A promissory note will pay \$30, 000 at maturity 10 years from now. How much should you pay for the note now if the note gains value at a rate of 6% compounded continuously? WW";a.V._......_.______;__.__..._....tmm.tw‘Wan..Inmm.W.wamewm \ 7. (20 points) a) A regular pentagon is inscribed in a circle of radius 1 ' ft. 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 ﬁx): tan(-:-—g). 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 y = 7— 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? 10) (10 points) Give domain, range and a good sketch of the graph of the inverse function y = sin“(x~—1) 11. (15 points) Solve the following triangle: <A = 73°, <13 :28“, 0:42ft mm;awm.@.mmcmmmmwwgw_wxm 12. (15 points) For the rational function f(x)= w do the x—4 following: a) Find all x—intercepts (if any) h) Find all y-intercept. ' c) Find all vertical asymptotes. d) Find the horizontal asymptote. e) Sketch the graph (label the axes, asymptotes and all intercepts): 13. (10 points) Evaluate each expression: a) Given sect = ——2, and tant > 0, ﬁnd Siﬂ(t) b) Given sin(9) = %,0" <9 < 900 ,ﬁnd sin(90° —9) c) cow—120°) 14. (15 points) Extra Credit 3.) Compute the ﬁrst four terms of the sequence ah = 2” n+1 ' b) Rewrite the following sum using )3 (sigma) notation: c) Find the sum of the following geometric series: d) Find a fraction equivalent of .45454545454545454545454545. ...
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## This note was uploaded on 08/09/2011 for the course MATH 3 taught by Professor Staff during the Spring '08 term at UCSC.

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Practice Final Fall 2010 - MATH 3 FINAL Instructor N andini...

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