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

Which one of the following is correct regarding $\rm \lim\limits_{x\rightarrow 3}\frac{|x-3|}{x-3}$?

What is $\rm \lim\limits_{x\rightarrow \frac{\pi}{2}}(\sec \theta-\tan \theta)$ equal to? 

Direction : Consider the following for the items that follow :

Let f(x) = |x|² - |x²|

Consider the following statements : 

I. f(x) is continuous at x = 0. 

Il. f(x) is continuous at x = 1 

Which of the statements given above is/are correct?