Question

limx→0x×tanx/根号(1-x^2)-1

Answer 1

x×tanx/[sqrt(1-x^2)-1]
=x^2/[sqrt(1-x^2)-1]
=x^2/-0.5x^2=-2

Answer 2

lim(tanx/x)^(1/x²)
=lim[1+(tanx-x)/x]^(1/x²)
=lim{[1+(tanx-x)/x]^[x/(tanx-x)]}^[(tanx-x)/x³]
=lime^[(tanx-x)/x³]
=e^lim(sec²x-1)/(3x²)
=e^limtan²x/(3x²)
=e^(1/3)

Answer 3

x=0