Q. 45 - Calculus

Question

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

$\underset{x\to 2}{\lim }\frac{3}{4-2^x}$

Step-by-Step Solution

Answer

The value of the limit does not exist.

Step 1. Given information.

The given function is $\underset{x\to 2}{\lim }\frac{3}{4-2^x}$

Step 2. Value of the limit.

Consider the table,

$x$	$1.9$	$1.99$	$1.999$	$2$	$2.001$	$2.01$	$2.1$
$\frac{3}{4-2^x}$	$11.199$	$108.57$	$1082.39$		$-1081.64$	$-107.82$	$-10.44$

The value of $\frac{3}{4-2^x}$ approaches to $\infty ,-\infty$ to the left and right respectively.

Therefore, the limit does not exist.