lim[x→1] (sinπx)/(x-1)=(0/0)=lim[x→1] (sinπx)'/(x-1)'=lim[x→1] -π*cos(πx)=π
lim[x→∞] (logx)/(x^2)=(∞/∞)=lim[x→∞] (logx)'/(x^2)'=lim[x→∞] 1/(2x^2)=0