Chapter 11.1, Problem 7E

To determine

To complete: the table, estimate the limit and determine whether the limit reaches or not.

Answer to Problem 7E

$x$	$1.9$	$1.99$	$1.999$	$2$	$2.001$	$2.01$	$2.1$
$f\left(x\right)$	$13.5$	$13.95$	$13.995$	$14$	$14.005$	$14.05$	$14.5$

The limit can be reached

  $\underset{x\to 2}{\lim }f\left(x\right)=14$

Explanation of Solution

Given:

  $\underset{x\to 2}{\lim }\left(5x+4\right)$

$x$	$1.9$	$1.99$	$1.999$	$2$	$2.001$	$2.01$	$2.1$
$f\left(x\right)$				?

Calculation:

Substitute the x values in the given limit.

Thus,

$x$	$1.9$	$1.99$	$1.999$	$2$	$2.001$	$2.01$	$2.1$
$f\left(x\right)$	$13.5$	$13.95$	$13.995$	$14$	$14.005$	$14.05$	$14.5$

  $\begin{array}{l}\underset{x\to 2}{\lim }(5x+4)=5(2)+4\\ =10+4\\ =14\end{array}$

This limit can be reached since $f$ is a polynomial function

Conclusion:

This limit can be reached and the value of the limit is $\underset{x\to 2}{\lim }f\left(x\right)=14$