What is $$\mathop {\lim }\limits_{x \to 0} {e^{ - {1 \over {{x^2}}}}}$$ equal to ?

Consider the function $$f(x) = \left| {x - 1} \right| + {x^2}$$ where x $$\in$$ R, then which one of the following statements is correct?

A function is defined as follows

$$f(x) = \left\{ {\matrix{ { - {x \over {\sqrt {{x^2}} }},} & {x \ne 0} \cr {0,} & {x = 0} \cr } } \right.$$

Which one of the following is correct in respect of the above function?

Consider the following statements

1. $$x + {x^2}$$ is continuous at x = 0

2. $$x + \cos {1 \over x}$$ is discontinuous at x = 0

3. $${x^2} + \cos {1 \over x}$$ is continuous at x = 0

Which of the above are correct?