Lim (√(2x²+1) -x) = Lim (√(2x²+1) -x)*(√(2x²+1) +x)/ (√(2x²+1) +x)=
x→+∞ ..
Lim(2x²+1) -x²) / (√(2x²+1) +x) =Lim (x²+1) / (√(2x²+1) +x) =
Lim(x+1/x) / (√(2+1/x²) +1) = +∞.
* * * * * *
Lim (x² +x -12) / (x² +2x -8) =Lim (x +4)(x-3) / (x +4)(x-2) =
x→-4---------------------------- x→-4
Lim (x-3) / (x-2) = (-4 -3)/(-4-2) =7/6.
x→-4