Question

True or False If f is continuous at c, then$\underset{x\to c^{+}}{\lim }f\left(x\right)=f\left(c\right)$.

Short answer

The answer is True.

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,

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

or,

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

or,

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

So, from this equation it is clear that the above statement is true.