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Chapter 1: Q. 21 (page 149)

鈭�0that approaches (a)1,(b)2,(c)鈭�.

Short Answer

Expert verified

鈭�0approaches to (a)1.

Step by step solution

01

Step 1. Given information

The given information is鈭�0, we need to write鈭�0approaches to (a)1,(b)2,(c)鈭�.

02

Step 2. The explanation for the correct option

For example, limx鈫�鈭�x1x.

=limx鈫�鈭�elnx1x.

=limx鈫�鈭�elnxx.

=elimx鈫�鈭�elnxx.

=elimx鈫�鈭�1x1.(Applying the L-Hospital rule).

=e0.

=1.

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Most popular questions from this chapter

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.

Write each of the inequalities in interval notation:

x2-1+3<0.5

If fis a continuous function, what can you say aboutlimx鈫�1f(x)?

Write delta-epsilon proofs for each of the limit statements limx鈫�cfx=Lin Exercises 47-60.

limx鈫�-6x+2=-4.

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�-1-f(x)=2,limx鈫�-1+f(x)=2,f(-1)=1.
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