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lim(x→∞)(x-4/x+3)^x极限?详细点有的变形我看不懂
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lim(x→∞)(x-4/x+3)^x 极限?详细点 有的变形我看不懂
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答案和解析
lim(x→∞)(x-4/x+3)^x
=lim(x→∞)[(x-4)/(x+3)]^x
=lim(x→∞)[(x+3-7)/(x+3)]^x
=lim(x→∞)[(1-7/(x+3)]^x
=lim(x→∞)[(1-7/(x+3)]^[(x+3)/7*x*7/(x+3)]
=lim(x→∞)[(1-7/(x+3)]^[(x+3)/7]^[7x/(x+3)] 【lim(x→∞)(1-1/x)^x=1/e】
=lim(x→∞)(1/e)^[7x/(x+3)]
=lim(x→∞)(1/e)^[7/(+3/x)]
=1/(e^7)
=lim(x→∞)[(x-4)/(x+3)]^x
=lim(x→∞)[(x+3-7)/(x+3)]^x
=lim(x→∞)[(1-7/(x+3)]^x
=lim(x→∞)[(1-7/(x+3)]^[(x+3)/7*x*7/(x+3)]
=lim(x→∞)[(1-7/(x+3)]^[(x+3)/7]^[7x/(x+3)] 【lim(x→∞)(1-1/x)^x=1/e】
=lim(x→∞)(1/e)^[7x/(x+3)]
=lim(x→∞)(1/e)^[7/(+3/x)]
=1/(e^7)
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