Question

设f(x)在x=0处可导且f(x)=0:求limx趋近于0,f(1－cosx)/tan(x^2)

Answer 1

limx趋近于0,f(1－cosx)/tan(x^2)

=limx趋近于0,f(1－cosx)-f(0)/(x^2)

=limx趋近于0,f(1－cosx)-f(0)/(1-cosx) × (1-cosx)/(x^2)

=f'(0)×limx趋近于0 (1-cosx)/(x^2)

=f'(0)×limx趋近于0 (x^2/2)/(x^2)

=f'(0)/2