   Chapter 2.6, Problem 79E

Chapter
Section
Textbook Problem

Use Definition 9 to prove that lim x → ∞ e x = ∞ . Definition 9 To determine

To prove: The value of limit of the function limxex=.

Explanation

Definition used:

Let f be a function defined on some interval (a,).

Then limxf(x)= means that for every positive number M there is a corresponding positive number N such that if x>N then f(x)>M.

Graph:

Proof:

Let the function f(x)=ex

Let M=ex1 some x1 is any real number.

M=ex1ln(M)=ln(ex1)ln(M)=x1

Choose N=ln(M) depends on M

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