Right-hand limit, Left-hand limit

Exercise

1.

Find the limit of the follwing functions.．

(a)

$${\lim_{x \rightarrow 0}\frac{1}{x}}$$

(b)

$${\lim_{x \rightarrow 0}\frac{1}{x^{2}}}$$

(c)

$${\lim_{x \rightarrow 0+}\frac{\vert x\vert}{\sqrt{a+x} - \sqrt{a-x}}}$$

(d)

$${\lim_{x \rightarrow 0-}\frac{x}{\sqrt{1-\cos{x}}}}$$

(e)

$${\lim_{x \rightarrow \infty}\cos{\frac{1}{x}}}$$

(f)

$${\lim_{x \rightarrow \infty}\frac{\sin{x}}{x}}$$

(g)

$${\lim_{x \rightarrow 0+}\cos{\frac{1}{x}}}$$