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Chapter 3: Q. 30 (page 311)

Calculate each of the limits in Exercises 21-48. Some of these limits are made easier by L'H么pital's rule, and some are not.

limx鈫�0+x-1-12x-1

Short Answer

Expert verified

The value of limit isln2-1ln2

Step by step solution

01

Step 1. Given information

Given functionlimx鈫�0+x-1-12x-1

02

Apply L-Hospital rule and solve

Calculating, we get

limx鈫�0+x-1-12x-1=limx鈫�0+1x-12x-1limx鈫�0+x-1-12x-1=limx鈫�0+2x-1-xx2x-1limx鈫�0+x-1-12x-1=limx鈫�0+2x-1-xx路2x-x=limx鈫�0+2xln2-0-1x路2xln2+2x路1-1=limx鈫�0+2xln2-1x路2xln2+2x-1=20ln2-10路20ln2+20-1=ln2-1ln2+1-1=ln2-1ln2

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Most popular questions from this chapter

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.

f(x)=x2(x-1)(x+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)=1-x4-2

Restate the Mean Value Theorem so that its conclusion has to do with tangent lines.

Explain the difference between two antiderivatives of the function.

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)=(x鈭�2)(x+2)
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