Question

Find the limit lim(x=2) (x3-2x2+4x-8)/(x4-2x3+x-2)

Answer 1

first substitute x=2 in above we get 0/0
apply l hospital rule
3x^2 -2(2x)+4/4x^3 -2(3x^2) +1
3x^2 -4x+4/4x^3 -6x^2+1
apply x=2
3(2)^2 -4(2)+4/4(2)^3 -6(2)^2+1
3(4)-8+4/32-24+1
12-4/8+1
8/9 is answer