Question

limx→1(√(3-x)-√(1+x))/(x²-1)

limx→0 (x^2-1)/[√(3-x)-√(1+x)]=?
是怎么解的,
错了,是"x→1".

Answer 1

lim[x→1](x^2-1)/[√(3-x)-√(1+x)]
= lim[x→1](x^2-1)[√(3-x)+√(1+x)]/[(3-x)-(1+x)]
= lim[x→1](x+1)(x-1)[√(3-x)+√(1+x)]/2(1-x)
= lim[x→1](x+1)[√(3-x)+√(1+x)]/(-2)
= -2√2