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Chapter 3: Q. 40 (page 311)

Calculate each of the limits in Exercises 21-48. Some of these limits are made easier by L鈥橦opital鈥檚 rule, and some are not.

limx鈫�0+lnxlnx-x+1.

Short Answer

Expert verified

The value of the limitlimx鈫�0+lnxlnx-x+1is,0.

Step by step solution

01

Step 1. Given information

limx鈫�0+lnxlnx-x+1.

02

Step 2. The limit is given below:

limx鈫�0+lnxlnx-x+1=limx鈫�0+1x1x-1[L'Hopital's rule]

role="math" localid="1648717401268" =limx鈫�0+11-xx=limx鈫�0+x1-x=0

The exact value is, 0.

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Most popular questions from this chapter

Find the critical points of the function

f'(x)=1+x2-4

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.

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Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.

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Find the possibility graph of its derivative f'.

Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility.

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