lim(4/4-x)的4/X次X→0 求函数极限
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4/(4-x)
= [(4-x) + x]/(4-x)
= 1 + x/(4-x)
= 1 + 1 / [(4-x) / x]
原式 = lim(x->0) { 1 + 1 / [(4-x) / x)] }^[(4-x)/x * x/(4-x) * 4/x]
基于重要极限lim(y->0) (1+1/y)^y,这里y = (4-x)/x,前提是1/[(4-x)/x] = 1/(4/x-1) -> 0
= e^lim(x->0) 4/(4-x)
= e^[4/(4-0)]
= e^(4/4)
= e
= [(4-x) + x]/(4-x)
= 1 + x/(4-x)
= 1 + 1 / [(4-x) / x]
原式 = lim(x->0) { 1 + 1 / [(4-x) / x)] }^[(4-x)/x * x/(4-x) * 4/x]
基于重要极限lim(y->0) (1+1/y)^y,这里y = (4-x)/x,前提是1/[(4-x)/x] = 1/(4/x-1) -> 0
= e^lim(x->0) 4/(4-x)
= e^[4/(4-0)]
= e^(4/4)
= e
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