Math150Sols1and2S11

Math150Sols1and2S11 - QUIZ ON CHAPTERS 1 AND 2 SOLUTIONS...

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QUIZ ON CHAPTERS 1 AND 2 SOLUTIONS MATH 150 – SPRING 2011 – KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% Show all work, simplify as appropriate, and use “good form and procedure” (as in class). Box in your final answers! No notes, books, or calculators allowed. 1) Fill in the blanks. Find rules for functions f and g so that f ± g () x = fgx = 1 x + 4 3 . (We are decomposing a composite function.) gx = x + 4 fu = 1 u 3 (Do not let f or g be the identity function.) (2 points) There are different possible answers, but the above would be a reasonable choice. 2) Complete the Identities. Fill out the table below so that, for each row, the left side is equivalent to the right side, based on the type of ID given in the last column. (10 points total; 2 points each) Left Side Right Side Type of ID 1 + cot 2 x csc 2 x Pythagorean ID cos u + v cos u cos v ± sin u sin v Sum ID sin u ± v sin u cos v ± cos u sin v Difference ID sin 2 u 2sin u cos u Double-Angle ID cos 2 u 1 + cos 2 u 2 or 1 2 + 1 2 cos 2 u Power-Reducing ID (PRI)
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3) Write any two of the three different versions of the Double-Angle Identity for cos 2 u () that were listed in Chapter 1. (4 points) Any two of these three: Version 1: cos 2 u = cos 2 u ± sin 2 u Version 2: cos 2 u = 1 ± 2sin 2 u Version 3: cos 2 u = 2cos 2 u ± 1 The Pythagorean identity sin 2 u + cos 2 u = 1 can be used to get from Version 1 to either of the other two versions. 4) Fill out the table below. Use interval form (the form using parentheses and/or brackets) except where indicated. You do not have to show work. (6 points total; 1 point each) fx Domain Range cos x ±² , ² ± 1, 1 ² ³ ´ µ tan x Use set-builder form. x ± ± x ² ³ 2 + nn ± ² ´ µ · ¸ ¹ º , ² csc x Use set-builder form. x ± ± x ² ± ² {} , ± 1 ( ³ ´ µ 1, ² · )
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5) Verify the identity sin 2 x () 1 + tan 2 x = 2sin x cos 3 x using the identities in Chapter 1. (6 points) sin 2 x 1 + tan 2 x = x cos x sec 2 x ± by a Double-Angle ID ± by a Pythagorean ID = x cos x 1 sec 2 x ² ³ ´ µ · = x cos x cos 2 x by a Reciprocal ID = x cos 3 x Q.E.D. When evaluating limits, give a real number, ± , ±² , or DNE (Does Not Exist).
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This note was uploaded on 09/08/2011 for the course MATH 150 taught by Professor Bart during the Spring '06 term at Mesa CC.

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Math150Sols1and2S11 - QUIZ ON CHAPTERS 1 AND 2 SOLUTIONS...

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