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

Consider the following for the two (02) items that follow:

$\text{Let } f(x)= \begin{cases} x^3, & x^2 < 1 \\ x^2, & x^2 \ge 1 \end{cases} \\$

What is  $\lim_{x \to 0} f'(x)$ equal to?