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Chapter 1: Q. 92 (page 151)

Prove the k=1 case of the first part of Theorem 1.31(b): that limx鈫�鈭�ex=鈭�. (Hint: Given M>0, choose N=lnM. Then if x>N=lnM, we must have x=lnM+c for some positive number c. Use this to show that ex>M.)

Short Answer

Expert verified

The first part of Theorem 1.31(b) is proved.

limx鈫�鈭�ex=鈭�

Step by step solution

01

Step 1. Given Information

We are given a theorem 1.31(b),

limx鈫�鈭�ex=鈭�

02

Step 2. Proving the statement.

Proving the statement,

For x>N,

x>lnMx=lnM+cex=elnM+cex=Mecxk>M

Since 'M' is arbitrary. This implies that limx鈫�鈭�ex=鈭�.

Hence Proved.

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