14.The functiont(x) = 2x−|x−3|x−3has
A)a removable discontinuity atx= 3.B)an infinite discontinuity atx= 3.C)a jump discontinuity atx= 3.D)no discontinuities.E)a removable discontinuity atx= 0 and an infinite discontinuity atx= 3.15.Find the values ofcso that the functionh(x) =c2−x2x <2x+cx≥2is continuous everywhere.

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CHAPTER 1.LIMITS33A.P. Calculus Test OneSection TwoFree-ResponseCalculators AllowedTime—45 minutesNumber of Questions—3Each of the three questions is worth 9 points. The maximum possible points earned onthis section is 27, which represents 50% of the total test score. There is no penalty forguessing.•SHOW ALL YOUR WORK. You will be graded on the methods you use as well asthe accuracy of your answers. Correct answers without supporting work may notreceive full credit.•Write all work for each problem in the space provided. Be sure to write clearly andlegibly. Erased or crossed out work will not be graded.•Justifications require that you give mathematical (non-calculator) reasons and thatyou clearly identify functions, graphs, tables, or other objects that you use.•You are permitted to use your calculator to solve an equation or graph a func-tion without showing work. However, you must clearly indicate the setup of yourproblem.•Your work must be expressed in mathematical notation rather than calculator syn-tax. For example,y=x2may not be written asY1=X^2.•Unless otherwise specified, answers (numeric or algebraic) need not be simplified.If your answer is given as a decimal approximation, it should be correct to threeplaces after the decimal point.Good Luck!NAME:

34The AP CALCULUS PROBLEM BOOK1.Consider the functionf(x) =|x|(x−3)9−x2.a)What is the domain off? What are the zeros off?b)Evaluate limx→3f(x).c)Determine all vertical and horizontal asymptotes off.d)Find all the nonremovable discontinuities off.2.Consider the functiong(x) =xxwith domain (0,∞).a)Fill in the following table.x0.010.10.20.30.40.51xxb)What islimx→1−g(x) ? What islimx→0+g(x) ?c)What do you think the smallest value ofg(x) is for values in the interval (0,1) ? Justifyyour answer.d)Find the average rate of change ofg(x) fromx= 0.1 tox= 0.4.3.Consider the functionF(x) = (a−1−x−1)−1whereais a positive real number.a)What is the domain ofF? What are the zeros ofF?b)Find all asymptotes ofFand discuss any discontinuities ofF.c)Evaluate limx→0F(x), limx→∞F(x), and limx→aF(x).d)For what value ofawillF(6) = 12 ?

CHAPTER2DERIVATIVES35

36The AP CALCULUS PROBLEM BOOK2.1Negative and Fractional ExponentsRewrite each expression with fractional exponents and simplify.