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^-#)