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Chapter 3: Q. 15 (page 310)

Calculate each of the limits in Exercises 15鈥�20 (a) using L鈥橦么pital鈥檚 rule and (b) without using L鈥橦么pital鈥檚 rule.

15.limx鈫�1x2+x-2x-1

Short Answer

Expert verified

The value of the limit is3

Step by step solution

01

Part (a) Step 1. Given information

We have been given the limit aslimx鈫�1x2+x-2x-1

02

Part (a) Step 2. Find the limit using L’Hôpital’s rule.

limx鈫�1x2+x-2x-1=limx鈫�12x+11=21+1=3

03

Part (b) Step 1. Find the limit without using L’Hôpital’s rule.

limx鈫�1x2+x-2x-1=limx鈫�1x2+2x-x-2x-1=limx鈫�1xx+2-1x+2x-1=limx鈫�1x+2x-1x-1=limx鈫�1x+2=1+2=3

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Most popular questions from this chapter

Find the possibility graph of its derivative f'.

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

f(x)=lnx2+1

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

f(x)=exx

Find the possibility graph of its derivative f'.

Determine the graph of a function f from the graph of its derivative f'.
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