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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 Xaxis 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 yintercept. ' 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.
 Spring '08
 STAFF

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