chpt - 5 CT3

In Q5.16 of the we get the Moment generating function for the uniform distribution. But when equating t=0 the answer is not equal to 1.
How is this possible? Please someone help.

Thanks in advance.

 

You need to compute lim Mx(t) as t -> 0.

To get the limit, you need to use the L'Hôpital's rule. Once you do that, you will get the limit as 1.

 

But why to compute the limits here?
Is this because direclty putting t=0 is giving infinity?

 

It has to be in limit as you should not be merely replacing t with 0 in the denominator. This is the correct way to do things.

 

Ok now I understand.
Thanks for your help.