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Chapter 3: Q. 22 (page 310)

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

limx鈫�1x-1ex-1-1

Short Answer

Expert verified

The value oflimx鈫�1x-1ex-1-1=1

Step by step solution

01

Step 1. Given information

The given limitlimx鈫�1x-1ex-1-1

02

Step 2. Using L’Hopital’s rule find the value of given limit

The limit using L鈥橦opitals rule is given below:

limx鈫�1x-1ex-1-1=limx鈫�11-0ex-1(1-0)-0[usingL'Hopitalsrule]=limx鈫�11ex-1=1e1-1=1e0=11=1

Therefore,the value of liimit1

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Most popular questions from this chapter

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

Determine whether or not each function fsatisfies the hypotheses of the Mean Value Theorem on the given interval [a,b]. For those that do, use derivatives and algebra to find the exact values of all c鈭�(a,b)that satisfy the conclusion of the Mean Value Theorem.

f(x)=tanx,[a,b]=[-蟺,蟺].

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

role="math" localid="1648368106886" f(x)=sin(蟺2x)

Use the definitions of increasing and decreasing to argue that f(x)=x4 is decreasing on (鈭�鈭�,0] and increasing on [0,鈭�). Then use derivatives to argue the same thing.

Find the possibility graph of its derivative f'.
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