高数B 求[(5x+2)/(5x-3)]^(2x+1),x趋近于无穷的极限
问题描述：
高数B 求[(5x+2)/(5x-3)]^(2x+1),x趋近于无穷的极限
答
原式=[1+5/(5x-3)]^(2x+1)
=[1+5/(5x-3)]^[(5x-3)/5*5(2x+1)/(5x-3)]
={[1+5/(5x-3)]^(5x-3)/5}^5(2x+1)/(5x-3)
=e^[5(2x+1)/(5x-3)]
=e^[5(2+1/x)/(5-3/x)]
=e^[5*(2+0)/(5-0)]
=e^2