Question

Show, using limits, that f(x)=x^2 -x +3, is continuous at x=2

Answer 1

Check if the left hand limit = right hand limit.
If it is, then limit exists.
Existence of limit at point a implies the function is continuous at point a.

Answer 2

Check if\[\lim_{x\rightarrow 2^+}f(x)=\lim_{x\rightarrow 2^-}f(x)\]

Answer 3

\[f(x)=\sin \frac{ 1 }{ x-1 }\]Use limits to determine if is continuous at x =1