How do you evaluate the limit of #lim (2x^2+5x+2)/(x^2+x-2)# as #x->-2#?
1 Answer
Dec 16, 2016
Explanation:
Start by factoring, because we are currently in indeterminate form
#=lim_(x->-2) (2x^2 + 4x + x+ 2)/((x+ 2)(x- 1))#
#=lim_(x-> -2) (2x(x + 2) + 1(x + 2))/((x + 2)(x - 1))#
#=lim_(x-> -2) ((2x+ 1)(x + 2))/((x +2)(x - 1))#
#= lim_(x-> -2) (2x + 1)/(x- 1)#
We can now evaluate.
#= (2(-2) + 1)/(-2 - 1)#
#=(-3)/(-3)#
#=1#
Hopefully this helps!
