设f(0)=0,f'(0)=6,求lim(x趋近于0)=(f(x-sinx))/x^3=?
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设f(0)=0,f'(0)=6,求lim(x趋近于0)=(f(x-sinx))/x^3=?
lim(x趋近于0)=(f(x-sinx))/x^3 (分子趋于f(0)=0分母趋于0,罗比达法则)
=lim(x->0) f'(x-sinx)*(1-cosx)/3x^2
=lim(x->0) f'(x-sinx)*lim(x->0) (1-cosx)/3x^2
=f'(0)*lim(x->0) {1-[1-2(sinx/2)^2}/3x^2
=6*lim (x->0) 2(sinx/2)^2/(3x^2)
=6*2*lim (x->0) (x/2)^2/(3x^2)
=6*2*1/12=1
=lim(x->0) f'(x-sinx)*(1-cosx)/3x^2
=lim(x->0) f'(x-sinx)*lim(x->0) (1-cosx)/3x^2
=f'(0)*lim(x->0) {1-[1-2(sinx/2)^2}/3x^2
=6*lim (x->0) 2(sinx/2)^2/(3x^2)
=6*2*lim (x->0) (x/2)^2/(3x^2)
=6*2*1/12=1
设f(0)=0,f'(0)=6,求lim(x趋近于0)=(f(x-sinx))/x^3=?
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