What is $$\mathop {\lim }\limits_{h \to 0} {{\sqrt {2x + 3h} - \sqrt {2x} } \over {2h}}$$ equal to ?

For what value of k is the function $$f(x) = \left\{ \matrix{ 2x + {1 \over 4},x < 0 \hfill \cr k,x = 0 \hfill \cr {\left( {x + {1 \over 2}} \right)^2},x > 0 \hfill \cr} \right.$$ continuous?

What is the value of $$\mathop {\lim }\limits_{x \to 0} {{\sin x^\circ } \over {\tan 3x^\circ }}$$ ?

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?