大师作文网求数列极限
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/10/02 12:18:00
求数列极限
1.显然0/0
洛必达
=[e^(x^2)*(x^2)'-0]/[(1)∫[0,x]e^(2t^2)dt+(2+x)e^(2x^2)]
=2xe^(x^2)/[(1)∫[0,x]e^(2t^2)dt+(2+x)e^(2x^2)]
还是0/0
再洛必达
=[2e^(x^2)+4x^2e^(x^2)]/[e^(2x^2)+e^(2x^2)+(2+x)*4xe^(2x^2)]
代入x=0
=[2+0]/[1+1+0]
=1
2.=lim n->无穷1/(n^2+n+1)+lim n->无穷1/(n^2+n+2)+lim n->无穷1/(n^2+n+n)
=0+0+0
=0
洛必达
=[e^(x^2)*(x^2)'-0]/[(1)∫[0,x]e^(2t^2)dt+(2+x)e^(2x^2)]
=2xe^(x^2)/[(1)∫[0,x]e^(2t^2)dt+(2+x)e^(2x^2)]
还是0/0
再洛必达
=[2e^(x^2)+4x^2e^(x^2)]/[e^(2x^2)+e^(2x^2)+(2+x)*4xe^(2x^2)]
代入x=0
=[2+0]/[1+1+0]
=1
2.=lim n->无穷1/(n^2+n+1)+lim n->无穷1/(n^2+n+2)+lim n->无穷1/(n^2+n+n)
=0+0+0
=0