Q:

Calculate limit for continuous function

I am having trouble with this question:
if f(x) is a continous function and $$ 1 - x^2 \leq f(x) \leq e^x $$ for all values of x, calculate $$ \lim_{x\to0} f(x) $$. 
Do I have to calculate the limit on both sides of $f(x)$?  How would I got about solving this? 

A:

A function $f$ with the given property cannot exist.  For $x=-\frac12$ we would have
$$ 0.75 = 1-(-1/2)^2 \le f(x) \le e^{-1/2} \approx 0.61 $$
but $0.75 \not\le 0.61$.

