lim(x趋向无穷)-(x+1)+√(x^2+1)
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lim(x趋向无穷)-(x+1)+√(x^2+1)
![lim(x趋向无穷)-(x+1)+√(x^2+1)](/uploads/image/z/16993215-63-5.jpg?t=lim%28x%E8%B6%8B%E5%90%91%E6%97%A0%E7%A9%B7%29-%28x%2B1%29%2B%E2%88%9A%28x%5E2%2B1%29)
如a^2-b^2=(a+b)(a-b) 原理
{根号(x^2+1)}^2-(x+1)^2=-2x={根号(x^2+1)+(x+1)}*{根号(x^2+1)-(x+1)}
所以原式=-2x/{根号(x*2+1)+(x+1)} 分子分母同时除以x 得
=-2/{根号(1+1/x^2)+1+1/x} x趋向无穷
=-1
{根号(x^2+1)}^2-(x+1)^2=-2x={根号(x^2+1)+(x+1)}*{根号(x^2+1)-(x+1)}
所以原式=-2x/{根号(x*2+1)+(x+1)} 分子分母同时除以x 得
=-2/{根号(1+1/x^2)+1+1/x} x趋向无穷
=-1
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