数学难题，怎么做？

⒈求极限⑴x→2lim(x²-5x+1)=2²-5*2+1=-5⑵x→+∞lim[√(x²+1)-√(x²-1)]=lim{[(x²+1)-(x²-1)]/[√(x²+1)+√(x²-1)]}=lim{2/[√(x²+1)+√(x²-1)]}=0⑶x→+∞lim(2+1/x+3/x²)=2+0+0=2⑷x→-1lim[1/(x+1)+2/(x²-1)]=lim[(x-1)/(x²-1)+2/(x²-1)]=lim[(x+1)/(x²-1)]=lim[1/(x-1)]=1/(-1-1)=-1/2⑸x→+∞lim[(2x²+x-1)/(4x³+x²+1)]=lim[(2/x+1/x²-1/x³)/(4+1/x+1/x³)]=(0+0-0)/(4+0+0)=0⑹x→+∞lim[(3x³+x²+1)/(5x³-x²)]=lim[(3+1/x+1/x³)/(5-1/x)]=(3+0+0)/(5-0)=3/5⑺x→0lim{x²/[1-√(1+x²)]}=lim{x²[1+√(1+x²)]/[1²-(1+x²)]}=-lim[1+√(1+x²)]=-[1+√(1+0)]=-2⑻x→1lim[(x³-1)/(x-1)]=lim(x²+x+1)=1+1+1=3⒉求常数a。x→+∞lim[(ax+2)/(2x-1)]=lim[(a+2/x)/(2-1/x)]=(a+0)/(2-0)=a/2∴a/2=3，a=6。