Practice Final (v2) Fall 2010

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

Info iconThis preview shows pages 1–17. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 16
Background image of page 17
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

Page1 / 17

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

This preview shows document pages 1 - 17. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online