just wondering if someoen could help me with this limit..:

Question

lim arctan[(x^2 - 4)/(3x^2-6x)]
x->2

Answer 1

My first step in doing limits is to sub in the approach value, this will give me Lim arctan (0/0)
This just about guarantees that the algebraic expression will factor and the offending factor will cancel.
Sure enough
lim arctan[(x^2 - 4)/(3x^2-6x)] x->2
= lim arctan[(x+2)(x-2)]/[3x(x-2)]
=lim arctan[(x+2)]/[3x]
= lim arctan(2/3)

now use your calculator, set to radian mode, to find
lim arctan[(x^2 - 4)/(3x^2-6x)] x->2
= .588

Answer 2

thanks for the reply... the question asks me to evaluate the limit using continuity, how do i justify my answer with continuity?

Answer 3

lim x^2+3x-4=6
x->2