Q. 40 - Calculus

Question

Use tables of values to make educated guesses for each of the limits in Exercises 39–52. 

$\underset{x\to 3^{+}}{\lim }\left(1-3x+x^2\right)$

Step-by-Step Solution

Answer

The value of $\underset{x\to 3^{+}}{\lim }\left(1-3x+x^2\right)$ is $1.$

Step 1. Given information.

The given limit function is $\underset{x\to 3^{+}}{\lim }\left(1-3x+x^2\right).$

Step 2. Table of values.

A table of values can be made as,

$x$	$3$	$3.001$	$3.01$	$3.1$
$1-3x+x^2$	*	$1.003001$	$1.0301$	$1.31$

Hence, $1-3x+x^2$ approaches to$1.$

Therefore,

$\underset{x\to 3^{+}}{\lim }\left(1-3x+x^2\right)=1$.