# Thread: Continuity of a trig/algibraic function

1. ## Continuity of a trig/algibraic function

I have a question in a past paper. Is the following continuous at x=0:
f(x)=$\displaystyle (1-cos(x))/x$
The model answer says no it is not continuous at x=0 and you would have to define f(0)=0 to make it continuous.

I understand that a/0 is undefined but in this case the numerator is 0 at the same x point that the denominator is thus we have 0/0. Is that still considered undefined and why?

Thanks

2. Originally Posted by Rowanmck
I have a question in a past paper. Is the following continuous at x=0:
f(x)=$\displaystyle (1-cos(x))/x$
The model answer says no it is not continuous at x=0 and you would have to define f(0)=0 to make it continuous.

I understand that a/0 is undefined but in this case the numerator is 0 at the same x point that the denominator is thus we have 0/0. Is that still considered undefined and why?

Thanks
Its still undefined because you're still trying to divide by 0.

3. Originally Posted by Rowanmck
I understand that a/0 is undefined but in this case the numerator is 0 at the same x point that the denominator is thus we have 0/0. Is that still considered undefined and why? Thanks
For ALL numbers $\displaystyle a$, $\displaystyle \dfrac{a}{b}$ is undefined if $\displaystyle b = 0$. It doesn't matter whether $\displaystyle a = 0$ or not.

4. Thanks for clearing that up for me :-)

5. ## L'Hopital's Rule

L'Hopital's Rule applies here.