Question

Lim (8x^3 -1)/(6x^2-5x+1)

x->1/2

Answer 1

6x²-5x+1=6(x-1/3)(x-1/2)=(2x-1)(3x-1)
d=25-24=1
x1=(5-1)/12=1/3
x2=(5+1)/12=1/2
lim(2x-1)(4x²+2x+1)/(2x-1)(3x-1)=lim(4x²+2x+1)/(3x-1)=(4*1/4 +2*1/2 +1)/(3*1/2 -1)=
=3:1/2=6