Calculus:Limits

$\lim _{x\to a}f(x)=L,$ When you see this equation it means you are try to let x approaches a.

You may have a question why can't we just write it as

$f(a)=L,$

some times we can't tell what is the F(a) equals to.

example 1

$\lim _{x\to a}f'(x)={x^{2}-1 \over x-1}$

But If a = 1 then you will get

$({1^{2}-1 \over 1-1})^{2}=({0 \over 0})^{2}$

Denominator can't be 0 so it is undefined at that point.

But in the graph if a = 1 it looks like it is than f'(x) = 4