Chapter 8.2, Problem 1QR

To determine

To calculate: The limit of the given function.

Answer to Problem 1QR

The obtained value is $1.1052$ .

Explanation of Solution

Given Information:

The function is defined as,

  $\underset{x\to \infty }{\lim }{\left(1+\frac{0.1}{x}\right)}^x$

Calculation:

Consider the given information,

  $\underset{x\to \infty }{\lim }{\left(1+\frac{0.1}{x}\right)}^x$

Make the table by using the given expression to intepret the limit.

$x$	${\left(1+\frac{0.1}{x}\right)}^x$
1	$1.1000$
10	$1.1046$
100	$1.1051$
1000	$1.1052$
10000	$1.1052$
100000	$1.1052$

Therefore, the limit of the sequence $1.1052$ as $x$ tends to infinite.