CalcExercisesCh1and2

# CalcExercisesCh1and2 - CALCULUS THE EXERCISES MATH 150...

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CALCULUS: THE EXERCISES MATH 150: CALCULUS WITH ANALYTIC GEOMETRY I VERSION 1.3 KEN KUNIYUKI and LALEH HOWARD SAN DIEGO MESA COLLEGE

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WEB SITE FOR FREE E-COPIES OF THESE MATERIALS http://www.kkuniyuk.com CONTACT INFORMATION Ken Kuniyuki: Website: http://www.kkuniyuk.com (course notes and sample exams are available) Email address: [email protected] Feel free to send emails with suggestions, improvements, tricks, etc.! I welcome them! LICENSING This work may be freely copied and distributed without permission under the specifications of the Creative Commons License. PARTIAL BIBLIOGRAPHY / SOURCES Calculus: Anton, Edwards/Penney, Larson, Stewart, Swokowski, Thomas People: Ken Kuniyuki, Laleh Howard, Tom Teegarden, and many more. “END OF CHAPTER” MARK Page E.1.3 is the last page of the Exercises for Chapter 1. Therefore, in the upper right hand corner, there is an additional period: “E.1.3.” This is to help people figure out if they have all the pages for a particular chapter.
(Exercises for Chapter 1: Review) E.1.1 CHAPTER 1: REVIEW FUNCTIONS 1) Assuming fx () = x 2 , evaluate f ± 4 , and evaluate (and expand) fa + h . 2) If ft = 4 t 5 ± 13 t + 4 , is f a polynomial function? Rational? Algebraic? 3) If gw = w ± 1 w 3 + 2 w ± 3 , is g a polynomial function? Rational? Algebraic? 4) If hx = x 3 ± x 2/5 , is h a polynomial function? Rational? Algebraic? 5) If = sin x , is f a polynomial function? Rational? Algebraic? DOMAIN AND RANGE 6) For each function rule below, write the domain of the corresponding function in interval form. a) = 7 x 9 + 4 x 6 ± 12 b) gt = t 2/3 + 4 c) hw = w ± 4 3 2 w 2 ± 3 w ± 2 d) = t + 2 t ± 5 e) = t ± 5 t + 2 f) = 7 ± x g) fr = r 2 ± 2 r ± 3 You may want to review Section 2.7 on Nonlinear Inequalities in the Precalculus notes. 7) Consider = x ± 2 . Graph y = . What is the domain of f in interval form? What is the range of f in interval form?

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(Exercises for Chapter 1: Review) E.1.2 SYMMETRY 8) If fx () = x 4 ± 3 x 2 + 4cos x , then the graph of y = in the usual xy -plane is symmetric about what? Why? (What kind of function is f ?) 9) If = 2 x 7 ± x ± 4sin x , then the graph of y = in the usual xy -plane is symmetric about what? Why? (What kind of function is f ?) 10) If gt = t 2/3 + 4 , then is the function g even, odd, or neither? 11) If hr = r tan r , then is the function h even, odd, or neither? 12) If = x 3 ± 2 x + 1 , then is the function f even, odd, or neither? COMPOSITIONS OF FUNCTIONS 13) Find rules for functions f and g so that f ± g x = fgx = x 4 + x 8 . (Do not let f or g be the identity function.) 14) Find rules for functions f and g so that f ± g t = fgt = 1 t 4 . (Do not let f or g be the identity function.) 15) Find rules for functions f and g so that f ± g r = fgr = sin r 2 . (Do not let f or g be the identity function.)
(Exercises for Chapter 1: Review) E.1.3. TRIG 16) Evaluate the following; write “undefined” when appropriate. a) cot ± b) sec c) csc 3 4 ² ³ ´ µ · d) sec 7 6 ² ³ ´ µ · e) sin 5 3 ² ³ ´ µ · f) tan 5 3 ² ³ ´ µ · 17) Verify the following trig IDs.

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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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CalcExercisesCh1and2 - CALCULUS THE EXERCISES MATH 150...

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