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

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1 Answer
Jan 8, 2018

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^-)