lim(x→∞)【(√ x²+x)-(2√ 2x²+2x)+x】等于多少?题中x²+x和2x²+2x都在根号下
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![lim(x→∞)【(√ x²+x)-(2√ 2x²+2x)+x】等于多少?题中x²+x和2x²+2x都在根号下](/uploads/image/z/8596373-5-3.jpg?t=lim%28x%E2%86%92%E2%88%9E%29%E3%80%90%EF%BC%88%E2%88%9A+x%26%23178%3B%2Bx%EF%BC%89-%EF%BC%882%E2%88%9A+2x%26%23178%3B%2B2x%EF%BC%89%2Bx%E3%80%91%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F%E9%A2%98%E4%B8%ADx%26%23178%3B%2Bx%E5%92%8C2x%26%23178%3B%2B2x%E9%83%BD%E5%9C%A8%E6%A0%B9%E5%8F%B7%E4%B8%8B)
lim(x→∞)【(√ x²+x)-(2√ 2x²+2x)+x】等于多少?题中x²+x和2x²+2x都在根号下
lim(x→∞)【(√ x²+x)-(2√ 2x²+2x)+x】等于多少?
题中x²+x和2x²+2x都在根号下
lim(x→∞)【(√ x²+x)-(2√ 2x²+2x)+x】等于多少?题中x²+x和2x²+2x都在根号下
整理一下,提个公因式.其它的都是常规办法
详见参考资料.
lim(x→-∞){[1-2^(3/2)]√ (x^2+x) + x} = -无穷
lim(x→+∞){[1-2^(3/2)]√ (x^2+x) + x}
=lim(x→+∞){[1-2^(3/2)]^2 (x^2+x) - x^2}/{[1-2^(3/2)]√ (x^2+x) - x}
=lim(x→+∞)【{[1-2^(3/2)]^2-1}x^2 + x[1-2^(3/...
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lim(x→-∞){[1-2^(3/2)]√ (x^2+x) + x} = -无穷
lim(x→+∞){[1-2^(3/2)]√ (x^2+x) + x}
=lim(x→+∞){[1-2^(3/2)]^2 (x^2+x) - x^2}/{[1-2^(3/2)]√ (x^2+x) - x}
=lim(x→+∞)【{[1-2^(3/2)]^2-1}x^2 + x[1-2^(3/2)]^2】/ {[1-2^(3/2)]√ (x^2+x) - x}
=lim(x→+∞)【{[1-2^(3/2)]^2-1}x + [1-2^(3/2)]^2】/ {[1-2^(3/2)]√ (1+1/x) -1}
=-无穷
lim(x→∞){[1-2^(3/2)]√ (x^2+x) + x} = -无穷
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lim(x→∞){[1-2^(3/2)]√ (x^2+x) + x} = -无穷