求极限 ①lim x→n- (x-[x]) ②lim x→e log(x-1)/x-e ③limx→0+ log x^x
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求极限 ①lim x→n- (x-[x]) ②lim x→e log(x-1)/x-e ③limx→0+ log x^x
①lim x→n- (x-[x]) n为任意自然数,[x]表示不大于X的最大整数
②lim x→e log(x-1)/x-e
③limx→0+ log x^x
②中, (log(x-1))/ x-e ,log的真数为x-1
②③中,log 底数皆为e
①lim x→n- (x-[x]) n为任意自然数,[x]表示不大于X的最大整数
②lim x→e log(x-1)/x-e
③limx→0+ log x^x
②中, (log(x-1))/ x-e ,log的真数为x-1
②③中,log 底数皆为e
①lim x→n- (x-[x])
=n-(n-1)
=1
②lim x→e ln(x-1)/(x-e)
=[lim x→e ln(x-1)*lim x→e [1/(x-e)]
=ln(e-1)*(+∞)
=+∞
③limx→0+ ln x^x
=limx→0+ (lnx)/(1/x)
=limx→0+ (1/x)/(-1/x²)
=limx→0+ (-x)
=0
=n-(n-1)
=1
②lim x→e ln(x-1)/(x-e)
=[lim x→e ln(x-1)*lim x→e [1/(x-e)]
=ln(e-1)*(+∞)
=+∞
③limx→0+ ln x^x
=limx→0+ (lnx)/(1/x)
=limx→0+ (1/x)/(-1/x²)
=limx→0+ (-x)
=0
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