Question

lim(x趋于0) (√(x^2+1)-1)/x,

Answer 1

lim(x->0) (√(x^2+1)-1)/x

=lim(x->0) (√(x^2+1)-1) (√(x^2+1)+1)/x (√(x^2+1)+1)

=lim(x->0) (x^2)/x (√(x^2+1)+1)

=lim(x->0) x/ (√(x^2+1)+1)

=0/2

=0