急求解4道关于极限的题目1.lim(1/(x+1)-3/(x^3+1)) (x趋向于-1)2.lim((1-cos3x)/x^2) (x趋向于0)3lim(((1+3x)/3x)^-2) (x趋向于无穷大)4.lim((1-3x)^(1/x)) (x趋向于0)要有解题过程
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![急求解4道关于极限的题目1.lim(1/(x+1)-3/(x^3+1)) (x趋向于-1)2.lim((1-cos3x)/x^2) (x趋向于0)3lim(((1+3x)/3x)^-2) (x趋向于无穷大)4.lim((1-3x)^(1/x)) (x趋向于0)要有解题过程](/uploads/image/z/9677243-11-3.jpg?t=%E6%80%A5%E6%B1%82%E8%A7%A34%E9%81%93%E5%85%B3%E4%BA%8E%E6%9E%81%E9%99%90%E7%9A%84%E9%A2%98%E7%9B%AE1.lim%281%2F%28x%2B1%29-3%2F%28x%5E3%2B1%29%29++++%28x%E8%B6%8B%E5%90%91%E4%BA%8E-1%292.lim%28%281-cos3x%29%2Fx%5E2%29+++%28x%E8%B6%8B%E5%90%91%E4%BA%8E0%293lim%28%28%281%2B3x%29%2F3x%29%5E-2%29++++%28x%E8%B6%8B%E5%90%91%E4%BA%8E%E6%97%A0%E7%A9%B7%E5%A4%A7%294.lim%28%281-3x%29%5E%281%2Fx%29%29++++%28x%E8%B6%8B%E5%90%91%E4%BA%8E0%29%E8%A6%81%E6%9C%89%E8%A7%A3%E9%A2%98%E8%BF%87%E7%A8%8B)
急求解4道关于极限的题目1.lim(1/(x+1)-3/(x^3+1)) (x趋向于-1)2.lim((1-cos3x)/x^2) (x趋向于0)3lim(((1+3x)/3x)^-2) (x趋向于无穷大)4.lim((1-3x)^(1/x)) (x趋向于0)要有解题过程
急求解4道关于极限的题目
1.lim(1/(x+1)-3/(x^3+1)) (x趋向于-1)
2.lim((1-cos3x)/x^2) (x趋向于0)
3lim(((1+3x)/3x)^-2) (x趋向于无穷大)
4.lim((1-3x)^(1/x)) (x趋向于0)
要有解题过程
急求解4道关于极限的题目1.lim(1/(x+1)-3/(x^3+1)) (x趋向于-1)2.lim((1-cos3x)/x^2) (x趋向于0)3lim(((1+3x)/3x)^-2) (x趋向于无穷大)4.lim((1-3x)^(1/x)) (x趋向于0)要有解题过程
如图,图片需要审核,稍安勿躁
-3
2
-1
e^3
lim[1/(x+1)-3/(x^3+1)] (x趋向于-1)
=lim[(x^2-x+1)/(x^3+1)-3/(x^3+1) ](x趋向于-1)
=lim[(x^2-x-2)/(x^3+1)](x趋向于-1)
=lim{(x-2)(x+1)/[(x+1)(x^2-x+1)]}(x趋向于-1)
=lim(x-2)/(x^2-x+1)(x趋向于-1)
...
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lim[1/(x+1)-3/(x^3+1)] (x趋向于-1)
=lim[(x^2-x+1)/(x^3+1)-3/(x^3+1) ](x趋向于-1)
=lim[(x^2-x-2)/(x^3+1)](x趋向于-1)
=lim{(x-2)(x+1)/[(x+1)(x^2-x+1)]}(x趋向于-1)
=lim(x-2)/(x^2-x+1)(x趋向于-1)
=(-1-2)/(1+1+1)
=-1
lim[(1-cos3x)/x^2] (x趋向于0)
=lim2[sin(3x/2)]^2/x^2] (x趋向于0)
=lim2(3x/2)]^2/x^2] (x趋向于0)
=9/2
lim[(1+3x)/3x]^(-2) (x趋向于无穷大)
=lim[(1+1/(3x)]^(-2) (x趋向于无穷大)
=[(1+0]^(-2)
=1
lim[(1-3x)^(1/x)] (x趋向于0)
=lim{(1-3x)^[1/(-3x)]}^(-3) (x趋向于0)
=e^(-3)
收起
第一题通分,第二题用等价无穷小替换,第三四题用重要极限。过程太难输入,你再问问身边的同学老师吧