Question

What is different about limx->c from limx->c- and limx->c+?

Answer 1

The limit as x approaches 'c' would be the exact value at f(c)

The limit as x approaches 'c' from the left (from the negative side) \(\large \lim_{x \rightarrow c^-}\) would be the value would be if we plug in values VERY close to (but not exactly) 'x' as long as they are smaller than c (since we are coming from the negative side)

And the limit as x approaches 'c' from the right (from the positive side) \(\large \lim_{x \rightarrow c^+}\)is what the value would be if we plug in values close to but not exactly 'c' that are bigger than 'c'

So for example

limit as x approaches 4....what does the function equal at x = 4?
Limit as x approaches 4 from the left side...what does the function equal if we plug in 3.9? 3.99? 3.99999 etc...

Limit as x approaches 4 from the positive side...what does the function equal if we plug in 4.01? 4.001? 4.00000001 etc..

Answer 2

Thanks for the fast reply!