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Chapter 1: Q. 5 (page 135)

Explain why we can鈥檛 calculate every limit limx鈫�cf(x) just by evaluating f(x) at x=c. Support your argument with the graph of a function f for which limx鈫�cf(x)=f(c).

Short Answer

Expert verified

We cannot calculate every limit limx鈫�cf(x) just by evaluating f(x) at x=c.

Step by step solution

01

Step 1. Given information.

We cannot calculate every limit limx鈫�cf(x)just by evaluating f(x) at x=c.

02

Step 2. Explanation.

For the limit expression limx鈫�1x-1x2-1, we cannot put x=1in the limit expression to get the value.

limx鈫�1x-1x2-1=1-112-1=01-1=00

So,00is undefined.

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Most popular questions from this chapter

Sketch the graph of a function f described in Exercises 27鈥�32, if possible. If it is not possible, explain why not.

f is left continuous at x = 1 and right continuous at x = 1, but is not continuous at x = 1, and f(1) = 鈭�2.

For each functionf graphed in Exercises23鈥�26, describe the intervals on whichf is continuous. For each discontinuity off, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.

limx鈫�43e1.7x+1

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(3-4x)=3

Each function in Exercises 9鈥�12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.

limx鈫�2-f(x)=-鈭�,limx鈫�2+f(x)=鈭�,f(2)=3.
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