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Chapter 1: Q. 42 (page 107)

For each limit statement in Exercises 41-44, use algebra to find 未or Nin terms of 蔚or M, according to the appropriate formal limit definition.

limx鈫�鈭�x-1x=1, findNin terms of蔚.

Short Answer

Expert verified

Forlimx鈫�鈭�x-1x=1,N=1蔚.

Step by step solution

01

Step 1. Given information

limx鈫�鈭�x-1x=1.

02

Step 2. From the limit expression,

fx=x-1xc=鈭�L=1

Now for localid="1648021305175" 蔚>0.

localid="1648021309449" x-1x-1=x-1-xx=-1x=1x<1N=蔚

Therefore, for x>N, we get localid="1648021314200" x-1x-1<蔚.

Hence,localid="1648021320692" N=1蔚.

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Most popular questions from this chapter

For each limit limx鈫�cf(x)=Lin Exercises 43鈥�54, use graphs and algebra to approximate the largest value of 未such that if localid="1648023101818" x鈭�(c-未,c)鈭�(c,c+未)thenf(x)鈭�(L-蔚,L+蔚)

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