已知y=y(X)是参数方程x=∫t/0arcsinu du,y=∫t/0te^u du,所确定的函数,求lim dy t-0 dx
人气:374 ℃ 时间:2019-08-20 23:32:33
解答
dy/dx
=(dy/dt)/(dx/dt)
=(te^t)/(arcsint).
当t趋近于0的时候,求极限符合罗必塔法则,则有:
limdy/dx
=lim (e^t+te^t)/[1/√(1-t^2)]
=e^0
=1.
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