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计算lim(ax+4/ax+1)的bx次方
题目详情
计算lim(ax+4/ax+1)的bx次方
▼优质解答
答案和解析
lim(x-->∞) [(ax + 4)/(ax + 1)]^bx
= lim(x-->∞) [1 + 3/(ax + 1)]^bx
= lim(x-->∞) [1 + 3/(ax + 1)]^[(ax + 1)/3 * 3/(ax + 1) * bx]
= exp lim(x-->∞) 3bx/(ax + 1)
= exp lim(x-->∞) 3b/(a + 1/x)
= exp [3b/(a + 0)]
= e^(3b/a)
= lim(x-->∞) [1 + 3/(ax + 1)]^bx
= lim(x-->∞) [1 + 3/(ax + 1)]^[(ax + 1)/3 * 3/(ax + 1) * bx]
= exp lim(x-->∞) 3bx/(ax + 1)
= exp lim(x-->∞) 3b/(a + 1/x)
= exp [3b/(a + 0)]
= e^(3b/a)
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