Question

True or False The limit of a rational function at$5$ equals the value of the rational function at$5$

Short answer

FALSE

Step-by-step solution

Step 1. Limit of a Quotient theorem

Limit of a Quotient:

$\underset{x\to c}{\lim }\left[\frac{f\left(x\right)}{g\left(x\right)}\right]=\frac{\underset{x\to c}{\lim }f\left(x\right)}{\underset{x\to c}{\lim }g\left(x\right)}$

where,$g\left(x\right)$is not equal to zero.

Step 2. Evaluating the given statement

The given statement " The limit of a rational function at $5$equals the value of the rational function at $5$" is False because it is not mentioned if the denominator of the rational function is non-zero.