Question

求limx趋于0 x-arcsinx/xln（1+x^2)

Answer 1

lim(x→0) (x-arcsinx)/xln（1+x^2)

=lim(x→0) (x-arcsinx)/x^3 (0/0)

=lim(x→0) [1-1/√(1-x^2)]/(3x^2)

=lim(x→0) [√(1-x^2)-1]/(3x^2*√(1-x^2))

=lim(x→0) [√(1-x^2)-1]/(3x^2) (0/0)

=lim(x→0) [-x/√(1-x^2)]/(6x)

=-1/6