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Page 119

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Q. 0

Page 148

Read the section and make your own sum-

mary of the material.

Q. 0

Page 119

Problem Zero: Read the section and make your own summary of the material.

Q. 0

Page 86

Read the section and make your own summary of material.

Q. 0

Page 97

Read the sections and make your own summary of the material.

Q. 0

Page 106

Read the section and make your own summary of the material.

Q. 0C

Page 134

Read the section and make your own summary of the material.

Q 1.

Page 86

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) A limit exists if there is some real number that it is equal to.

(b) The limit of fxas xcis the value fc.

(c) The limit of fxas xcmight exist even if the value of fcdoes not.

(d) The two-sided limit of fxas xcexists if and only if the left and right limits of fxexists as xc.

(e) If the graph of fhas a vertical asymptote at x=5, then limx5fx=.

(f) If limx5fx=, then the graph of fhas a vertical asymptote at x=5.

(g) If limx2fx=, then the graph of fhas a horizontal asymptote at x=2.

(h) Iflimxfx=2, then the graph offhas a horizontal asymptote aty=2.

Q. 1

Page 108

Explain why it makes intuitive sense thatlimxcx=c for any real number c. Then use a delta–epsilon argument to prove it.

Q. 1

Page 119

Finding roots of piecewise-defined functions: For each function f that follows, find all values x = c for which f(c) = 0. Check your answers by sketching a graph of f.

f(x)=4x2,ifx<0x+1,ifx0f(x)=x+1,ifx<04x2,ifx0f(x)=2x1,ifx12x2+x3,ifx>1

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