可以一下以下三道求极限的题吗?1.lim(x->无穷大)[x^3ln(x+1/x-1)-2x^2];答案:2/32.lim(x->无穷大)[xarctan(1/x)]^(x^2)答案:e^83.lim(x->0)[x^2+2xe^x+e^2x]^(2/sinx)答案:e^(-1/3)其中第一题为lim(x->无穷大)[(x^3)*
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![可以一下以下三道求极限的题吗?1.lim(x->无穷大)[x^3ln(x+1/x-1)-2x^2];答案:2/32.lim(x->无穷大)[xarctan(1/x)]^(x^2)答案:e^83.lim(x->0)[x^2+2xe^x+e^2x]^(2/sinx)答案:e^(-1/3)其中第一题为lim(x->无穷大)[(x^3)*](/uploads/image/z/8581322-2-2.jpg?t=%E5%8F%AF%E4%BB%A5%E4%B8%80%E4%B8%8B%E4%BB%A5%E4%B8%8B%E4%B8%89%E9%81%93%E6%B1%82%E6%9E%81%E9%99%90%E7%9A%84%E9%A2%98%E5%90%97%3F1.lim%28x-%3E%E6%97%A0%E7%A9%B7%E5%A4%A7%EF%BC%89%5Bx%5E3ln%28x%2B1%2Fx-1%29-2x%5E2%5D%3B%E7%AD%94%E6%A1%88%EF%BC%9A2%2F32.lim%28x-%3E%E6%97%A0%E7%A9%B7%E5%A4%A7%EF%BC%89%5Bxarctan%281%2Fx%29%5D%5E%28x%5E2%29%E7%AD%94%E6%A1%88%EF%BC%9Ae%5E83.lim%28x-%3E0%EF%BC%89%5Bx%5E2%2B2xe%5Ex%2Be%5E2x%5D%5E%282%2Fsinx%29%E7%AD%94%E6%A1%88%EF%BC%9Ae%5E%28-1%2F3%29%E5%85%B6%E4%B8%AD%E7%AC%AC%E4%B8%80%E9%A2%98%E4%B8%BAlim%28x-%3E%E6%97%A0%E7%A9%B7%E5%A4%A7%EF%BC%89%5B%28x%5E3%29%2A)
可以一下以下三道求极限的题吗?1.lim(x->无穷大)[x^3ln(x+1/x-1)-2x^2];答案:2/32.lim(x->无穷大)[xarctan(1/x)]^(x^2)答案:e^83.lim(x->0)[x^2+2xe^x+e^2x]^(2/sinx)答案:e^(-1/3)其中第一题为lim(x->无穷大)[(x^3)*
可以一下以下三道求极限的题吗?
1.lim(x->无穷大)[x^3ln(x+1/x-1)-2x^2];答案:2/3
2.lim(x->无穷大)[xarctan(1/x)]^(x^2)答案:e^8
3.lim(x->0)[x^2+2xe^x+e^2x]^(2/sinx)答案:e^(-1/3)
其中第一题为lim(x->无穷大)[(x^3)*(ln(x+1/x-1))-2x^2];答案:2/3
可以一下以下三道求极限的题吗?1.lim(x->无穷大)[x^3ln(x+1/x-1)-2x^2];答案:2/32.lim(x->无穷大)[xarctan(1/x)]^(x^2)答案:e^83.lim(x->0)[x^2+2xe^x+e^2x]^(2/sinx)答案:e^(-1/3)其中第一题为lim(x->无穷大)[(x^3)*
1.原式=lim[ln(x+1)-ln(x-1)-2/x]/(x^-3)
=lim[1/(x+1)-1/(x-1)+2/x^2]/(-3x^-4)(洛必达法则)
=lim[2/x^2-2/(x^2-1)]/(-3x^-4)
=lim[-2/(x^2(x^2-1))]/(-3x^-4)
=2/3limx^2/(x^2-1)=2/3
2.先求一个极限lim(x→∞)x^2[xarctan(1/x)-1]
=lim[arctan(1/x)-1/x]/(x^-3)
=lim[(-1/x^2)/(1+1/x^2)+1/x^2]/(-3x^-4)
=lim[1/(x^2(x^2+1))]/(-3x^-4)
=-1/3limx^2/(x^2+1)=-1/3
根据幂积函数的原理,原式=e^[limx^2(xarctan(1/x)-1)]=e^(-1/3)
3.原式=(x+e^x)^(4/sinx)
而lim(x→0)4(x+e^x-1)/sinx
=lim4(1+e^x)/cosx(洛必达法则)
=8
所以原式=e^8