In order for f to be continuous, must be equal to .
First I notice that and doesn't seem to be easy to calculate. Hence we must use the definition of limit to prove what they ask for.
I'm not sure about how to proceed, but you have to reach via a line and if it gives then try with a quadratic function. If it still gives , then you can suppose that the limit exists and is worth , hence the function to be continuous at . From it you would have to show that , such that if , then .
I'll wait for further help as well.