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Chapter 1: Q. 26 (page 88)

Consider the limit values below:

limx鈫�2-f(x)=鈭�,limx鈫�2+f(x)=-鈭�andf(2)=1

The strategy is to sketch the graph of the function having the above limit values

Short Answer

Expert verified

The graph obtained is

Step by step solution

01

Step 1. GIven

The given limit values are

limx鈫�2-f(x)=鈭�,limx鈫�2+f(x)=-鈭�andf(2)=1

02

Step 2. Graph obtained

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Most popular questions from this chapter

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 x鈫�cis the value fc.

(c) The limit of fxas x鈫�cmight exist even if the value of fcdoes not.

(d) The two-sided limit of fxas x鈫�cexists if and only if the left and right limits of fxexists as x鈫�c.

(e) If the graph of fhas a vertical asymptote at x=5, then limx鈫�5fx=鈭�.

(f) If limx鈫�5fx=鈭�, then the graph of fhas a vertical asymptote at x=5.

(g) If limx鈫�2fx=鈭�, then the graph of fhas a horizontal asymptote at x=2.

(h) Iflimx鈫�鈭�fx=2, then the graph offhas a horizontal asymptote aty=2.

For each limit statement , use algebra to find 未 > 0 in terms of 蔚> 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < 蔚.

limx鈫�0(5x2-1)=-1

For each limit statement, use algebra to find 未 or N in terms of 蔚or M, according to the appropriate formal limit definition.

limx鈫�鈭�2+鈥�(1+x+2)=1 find 未 in terms of 蔚.

Calculate each of the limits:

limx鈫�1xsin-1x2.

Write each of the inequalities in interval notation:

0<|x+3|<0.05
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