若函数fx在x=0处可导,又f(0)=0,求lim(x趋近于0) f(1-cosx)⼀tan(x2)……

2025-06-25 01:04:24
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回答1:

由洛必达法则,lim(x趋近于0) f(1-cosx)/tan(x2)=lim(x趋近于0) f'(1-cosx)*sinx/[-2x/cos(x^2)]
=[lim(x趋近于0)-cos(x^2)* f'(1-cosx)]*[[lim(x趋近于0)sinx/x]=-f"(0)/2=0.