设f(0)=0且f'(0)=2,求limx→0f(x)/sin2x
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设f(0)=0且f'(0)=2,求limx→0f(x)/sin2x
设f(0)=0且f'(0)=2,求limx→0f(x)/sin2x
设f(0)=0且f'(0)=2,求limx→0f(x)/sin2x
使用洛必达法则
limx→0f(x)/sin2x
=limx→0f‘(x)/(sin2x)'
=limx→0f'(x)/2cos2x
=2/2
=1
罗比达=fx'/2cosx=2/2=1
由洛比达法则:原式=f'(x)/(sin(2x)')=1
f'(0)=2,而(sin2x)'=2cosx,
所以,limx→0f(x)/sin2x=limx→0f‘(x)/(sin2x)'=limx→0 2/2cosx=2/2=1.
1
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