Question

How to find f(2) ? Help pls thanks!

Answer 1

f(2), or `lim_(x->2) f(x)`, is 4

Technically, f(2) is undefined since it encounters a division by 0 error.

The limit `lim_(x->2) f(x)`, however, equals 4

Explanation:

The limit `lim_(x->2) f(x)` is defined if `lim_(x->2^+) f(x)` and `lim_(x->2^-) f(x)` are both defined and equal

In this case, both limits are the same, and so you could just do the following

`lim_(x->2) f(x)`
`= lim_(x->2) (x^2(x-2))/(x-2)`
`= lim_(x->2) x^2` (since `x-2≠0` (technically) and thus you can cancel them out)
`=2^2=4`

(You will get the same result regardless if you try and evaluate it from either `x->2^+` or `x->2^-`)