Question

Examine the continuity of the following function at the given point
$F\left(x\right)=e^{5x}-e^{2x}$
$=1$
for $x\ne o$ at $x=0$
for $x=o$ at $x=0$

Answer 1

$f\left(x\right)=e^{5x}-e^{3x}=1RHL=li{m}_{x\to 0+}f\left(x\right)=0LHL=li{m}_{x\to 0-}f\left(x\right)=0f\left(0\right)=0$

As $RHL=LHL=f\left(0\right)$

The function is continuous at $x=0$