lim(x→∞)[(a x^2)/x+1]+bx=lim(x→∞)(a x^2)+bx(x+1) / x+1=lim(x→∞)(a+b)x^2+bx / x+1 //搞不懂,为什么就可以判定a+b=0了=2
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![lim(x→∞)[(a x^2)/x+1]+bx=lim(x→∞)(a x^2)+bx(x+1) / x+1=lim(x→∞)(a+b)x^2+bx / x+1 //搞不懂,为什么就可以判定a+b=0了=2](/uploads/image/z/11487293-53-3.jpg?t=lim%28x%E2%86%92%E2%88%9E%29%5B%28a+x%5E2%29%2Fx%2B1%5D%2Bbx%3Dlim%28x%E2%86%92%E2%88%9E%29%28a+x%5E2%29%2Bbx%28x%2B1%29+%2F+x%2B1%3Dlim%28x%E2%86%92%E2%88%9E%29%28a%2Bb%29x%5E2%2Bbx+%2F+x%2B1++++%2F%2F%E6%90%9E%E4%B8%8D%E6%87%82%2C%E4%B8%BA%E4%BB%80%E4%B9%88%E5%B0%B1%E5%8F%AF%E4%BB%A5%E5%88%A4%E5%AE%9Aa%2Bb%3D0%E4%BA%86%3D2)
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lim(x→∞)[(a x^2)/x+1]+bx=lim(x→∞)(a x^2)+bx(x+1) / x+1=lim(x→∞)(a+b)x^2+bx / x+1 //搞不懂,为什么就可以判定a+b=0了=2
lim(x→∞)[(a x^2)/x+1]+bx
=lim(x→∞)(a x^2)+bx(x+1) / x+1
=lim(x→∞)(a+b)x^2+bx / x+1 //搞不懂,为什么就可以判定a+b=0了
=2
lim(x→∞)[(a x^2)/x+1]+bx=lim(x→∞)(a x^2)+bx(x+1) / x+1=lim(x→∞)(a+b)x^2+bx / x+1 //搞不懂,为什么就可以判定a+b=0了=2
上下除以x
=[(a+b)x+b]/(1+1/x)
分母趋于1
而极限存在
所以分子野营趋于一个常数
而如果a+b≠0
则(a+b)x+b趋于无穷,不合题意
所以a+b=0
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