How do you evaluate the limit #(x^4+5x^3+6x^2)/(x^2(x+1)-4(x+1))# as x approaches -2?
1 Answer
Sep 16, 2016
1
Explanation:
direct substitution into the expression yields
#0/0# that is indeterminate form.Factorising numerator/denominator.
#(x^2(x^2+5x+6))/((x+1)(x^2-4))=(x^2cancel((x+2))(x+3))/((x+1)cancel((x+2))(x-2))#
#=(x^2(x+3))/((x+1)(x-2))#
#rArrlim_(xto-2)(x^4+5x^3+6x^2)/(x^2(x+1)-4(x+1))#
#=lim_(xto-2)(x^2(x+3))/((x+1)(x-2))#
#=(4(1))/((-1)(-4))=4/4=1#
