Consider the following statements in respect of the function $$f(x) = \sin \left( {{1 \over x}} \right)$$ for x $$\ne$$ 0 and f(0) = 0 :

1. $$\mathop {\lim }\limits_{x \to 0} f(x)$$ exits

2. f(x) is continuous at x = 0

hich of the above statement is/are correct?

$$\mathop {\lim }\limits_{x \to 0} {{1 - {{\cos }^3}4x} \over {{x^2}}}$$ is equal to

The value of k which makes $$f(x) = \left\{ {\matrix{ {\sin x,} & {x \ne 0} \cr {k,} & {x = 0} \cr } } \right.$$ continuous at x = 0, is

For the following two (02) items:
Let
$f(x)=\begin{cases}\frac{1-\cos 2x}{x^{2}}&,x<0\\ 9&,x=0\\ \frac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}&,x>0\end{cases}$

What is $\lim _{x\rightarrow 0^{-}}f(x)$ equal to?