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Chapter 1: Q. 44 (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�x2+2=鈭�,findNin terms ofM.

Short Answer

Expert verified

Forlimx鈫�鈭�x2+2=鈭�,N=M-2.

Step by step solution

01

Step 1. Given information

limx鈫�鈭�x2+2=鈭�.

02

Step 2. From the limit expression,

fx=x2+2c=鈭�L=鈭�

Now for 未>0.

x<Nx2<N2x2+2<N2+2x2+2<M

Therefore,

N2+2=MN2=M-2N=M-2

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