Limits and continuity

Find the limit of $$\lim_{x\rightarrow0}\ f\left(x\right)$$ .

Find the limit of $$\lim_{x\rightarrow-\frac{1}{2}}\ f\left(x\right)$$ .

Find the limit of $$\lim_{x\rightarrow-1^-}\ f\left(x\right)\ and\ \lim_{x\rightarrow-1^+}\ f\left(x\right)$$ .

Find the limit of $$\lim_{x\rightarrow0}\ f\left(x\right)$$ .

Find the limit of $$\lim_{x\rightarrow-1}\ \frac{\left(\sqrt[]{x\ +\ 10}\ -\ 3\right)}{x\ +\ 1}$$ .

Find the limit of $$\lim_{x\rightarrow0}\ \ \sqrt[4]{2\cos\left(x\right)-5}\$$ .

Find the limit of $$\lim_{x\rightarrow1^-}\ \ \ \frac{1}{x\ -\ 1}+e^{x^2}$$ .

Find the limit of $$\lim_{x\rightarrow0^+}\ \ \ \sin\frac{1}{x\ }$$ .

Find the limit of $$\lim_{x\rightarrow0^+}\ \ \ x\ \sin\frac{1}{x\ }$$ .

Find the limit of $$\lim_{x\rightarrow0^{ }}\ \ \ x^2\ \sin\frac{1}{x\ }$$ .

Where is the graph discontinuous?