Continuity Problem: Solutions & Resources

[DaalChawal]

 

[I like Serena]

A function is continuous at a point if its limit at that point is the same as its function value.

What is $\lim_{x\to 1} f(x)$ and what is $f(1)$?

 

[DaalChawal]

I'm getting $f(1)$ as well as $\lim_{x \to 1}f(x)$ = 0 both lhl and rhl

 

[I like Serena]

I'm getting $f(1)$ as well as $\lim_{x \to 1}f(x)$ = 0 both lhl and rhl

Then $f$ is continuous at $x=1$ and we have eliminated answer a.

The remaining question is what happens at other values of $x$.
Can we find another integer value for $x$ where $f$ is continuous?
Can we find a real $x$ where $f$ is not continuous?