lim (e^x+2xarctanx)/(e^x-πx) x->正无穷

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/05/01 03:05:36

lim (e^x+2xarctanx)/(e^x-πx) x->正无穷
π是pai

x—>正无穷时,分子分母同趋于正无穷
所以可以用洛必达法则
lim (e^x+2xarctanx)/(e^x-πx)
=lim (e^x+2arctanx+2x/(1+xx))/(e^x-π)
=lim (e^x+2xarctanx+0)/(e^x)
=lim (1+2xarctanx/(e^x))
=1+lim (2arctanx+2x/(1+xx))/(e^x)
=1+lim(2arctanx/e^x)
=1+lim(2/(1+xx) / e^x)
=1+0
=1

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