设f (x)在x=0处可导,且f (0)=0,求证:lim(x→∞)f (tx)-f (x)/x=(t-1)f' (0)
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设f (x)在x=0处可导,且f (0)=0,求证:lim(x→∞)f (tx)-f (x)/x=(t-1)f' (0)
设f (x)在x=0处可导,且f (0)=0,求证:lim(x→∞)f (tx)-f (x)/x=(t-1)f' (0)
设f (x)在x=0处可导,且f (0)=0,求证:lim(x→∞)f (tx)-f (x)/x=(t-1)f' (0)
确定是x→∞ 这样极限时0/∞型=0 如果是x→0有:
lim(x→0 )[f(tx)-f (x)]/x (0/0 洛必塔法则)
=lim(x→0 )[t*f'(tx)-f'(x)]
=t*f'(0)-f'(0) (代入x=0)
=(t-1)f'(0)
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