Limits

We have,

and

Since, is continuous at , we must have

Let


form ]
Now, by using L'Hospital Rule

Given,
} \\[2ex]
1 & \text{for }
\end{cases}\,...(i)\)
For to be continuous at

From E (i),
For to be continuous at

The above limit is equal to 1, when

i.e.

Let

form ]
Using by L'Hospital rule, we get

Given, ln
And
Now, from E (i), we get
ln
does not exist
and
exist.