求大佬帮我一下,如图,给下详解
1个回答
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设a=lim(1/x)^tanx
lna=limln(1/x)^tanx
=limtanxln(1/x)
=-limtanxlnx
=-limlnx/(cosx/sinx) 应用洛必达法则
=-lim(1/x)/(-1/sin²x)
=limsin²x/x)
=0
lim(1/x)^tanx=a=e^0=1
-------------------------------------------
当x->0时
(f(x-x²)-f(x))/x³
=-(1/x)(f(x-x²)-f(x))/(-x²)
=-(1/x)f'(x)
=-f'(x)/x
=-f"(0)
lna=limln(1/x)^tanx
=limtanxln(1/x)
=-limtanxlnx
=-limlnx/(cosx/sinx) 应用洛必达法则
=-lim(1/x)/(-1/sin²x)
=limsin²x/x)
=0
lim(1/x)^tanx=a=e^0=1
-------------------------------------------
当x->0时
(f(x-x²)-f(x))/x³
=-(1/x)(f(x-x²)-f(x))/(-x²)
=-(1/x)f'(x)
=-f'(x)/x
=-f"(0)
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