16x³-2
lim ----------------------------------
x→1/2 6x²-5x+1²
1. 6x²-5x+1²= 0
D= 25-24=1
x=(5+1)/12= 1/2
x=(5-1)/12= 1/3
6x²-5x+1²= 6*( x-(1/2))*( x-(1/3)) = 2*( x-(1/2))*3*( x-(1/3))= ( 2x- 1)*( 3x- 1)
16x³-2 2*(8x³-1) 2* (2x-1)(4x²+2x+1)
lim ---------------------- = -------------------------- = --------------------------------------------
x→1/2 6x²-5x+1² ( 2x- 1)*( 3x- 1) ( 2x- 1)*( 3x- 1)
2*(4x²+2x+1) 2*(4* 1/4 +2* 1/2+1 ) 6
= ----------------------- = -------------------------------- = --------------- = 12
( 3x- 1) 3* 1/2 - 1 1/2