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Expert-verified Found in: Page 889 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # True or False If f is continuous at c, then $\underset{x\to {c}^{+}}{\mathrm{lim}}f\left(x\right)=f\left(c\right)$.

See the step by step solution

## Step. 1 Continuous function

A function is said to be continuous at a point $x=c$, if its limit at $x=c$ exist and is equal to the absolute value of $f\left(x\right)$ at c.

## Step. 2 Solution

Let $f\left(x\right)$be continuous at $x=c$, then from above definition,

$\underset{x\to c}{\mathrm{lim}}f\left(x\right)=f\left(c\right),$

or,

$LHL=RHL=f\left(c\right)$,

or,

$\underset{x\to {c}^{-}}{\mathrm{lim}}f\left(x\right)=\underset{x\to {c}^{+}}{\mathrm{lim}}f\left(x\right)=f\left(c\right)$.

So, from this equation it is clear that the above statement is true. ### Want to see more solutions like these? 