# Limits and Continuity of a Piecewise Function

 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 11,722 You need to use parentheses to make it clear what you're doing. It looks like what you are doing is finding $$\lim_{x \to 5} \frac{\sqrt{(x+4)(x-4)}-3}{x-5}\cdot \frac{\sqrt{(x+4)(x-4)}+3}{\sqrt{(x+4)(x-4)}+3}$$ My first question to you is, why? I don't see why you have the x-5 in there. Look up the definition of continuity. You should see you're making this problem harder than intended. Or did you not describe f(x) correctly in the beginning of your post?