Limits of a function, epsilon delta approach

Question

$$\lim\limits_{x\to 2} x^2=4.$$

The answer is $4$, why not $3.98$ or a number other than $4$ - as in a number close to $4$. But why $4$.

I have only basic idea about limits, as in the denominator is not equal to zero, so direct substitution will work here. I tried understanding the epsilon delta approach, but I cannot get the clear picture.

Answer 1

In general if f(x) is is defined for x = a and is continuous around x = a, then $\lim_{x \to a} = f(a)$.

Answer 2

Abishek,

it says "there is delta, so that for every x in the delta-neighborhood of 2, the function $f(x)$ will be close to the limit". Since 2 belongs to the neighborhood, your value should be close to 4. But 3.9999 does not work, take $\epsilon = 0.00005$