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Applied MathCourse Code

APPM 1345Professor

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MidtermThis

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APPM 1345 Exam 1 Spring 2016

INSTRUCTIONS: Books, notes, and electronic devices are not permitted. Credit is

awarded for reasoning; therefore describe all your answers with legible and orderly ex-

planations, and BOX your ﬁnal answers.

1. Consider the function y=x−a2

x2−5and its graph.

(a) (3 points) If a= 5 then what is the domain of y?

(b) (5 points) If a= 0 then demonstrate why yis a decreasing function.

(c) (6 points) If a=4

√5, then describe any domain restrictions as asymptotes, holes,

or jump discontinuities.

(d) (5 points) If yhas a y-intercept at 2, then what must the value of abe?

2. Consider the function f(x) = x4−4x3+ 10

(a) (6 points) Name the relative extrema of f(x).

(b) (6 points) Name any points of inﬂection for f(x).

3. Each of the following problems are not related:

(a) (6 points) Name the critical points of sin(cos x) on [0,2π]

(b) (4 points) Name the general anti-derivative of y=x·x3

(c) (9 points) If pand qare integers and f(x) = (x−1)p(x+ 1)qfor p≥2 and

q≥2, then fhas three critical numbers; name them.

4. (8 points) Use Newton’s Method to estimate a root of x3−4x+ 4 = 0. Start with

an initial guess of x0= 1. Find x2and x101.

CONTINUED ON THE BACK

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