limit as x approaches 0 from the left of : e^(1/x) when x!=0. c when x= 0.

Find the value of c that will make function continuous

Question

limit as x approaches 0 from the left of : e^(1/x) when x!=0. c when x= 0.

Find the value of c that will make function continuous

anonymous · Answer

Do I find the limit as e^(1/x) approaches 0 from the left and let that eqaul c?

anonymous · Answer

$$f(x)=\begin{cases}
e^{1/x}&\text{for }x\not=0\
c&\text{for }x=0
\end{cases}$$
And you're asked to find $c$ that makes $f(x)$ continuous, i.e. such that $\displaystyle\lim_{x\to0^-}f(x)=c.$ Is that right?

anonymous · Answer

Wait, I have that wrong...

anonymous · Answer

There is no value of $c$ that makes the function continuous, since $\displaystyle\lim_{x\to0}f(x)$ doesn't exist.

Also, $\displaystyle\lim_{x\to0^-}f(x)=0$.