如图,求极限(定积分题目)
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如图,求极限(定积分题目)
![如图,求极限(定积分题目)](/uploads/image/z/5027908-4-8.jpg?t=%E5%A6%82%E5%9B%BE%2C%E6%B1%82%E6%9E%81%E9%99%90%EF%BC%88%E5%AE%9A%E7%A7%AF%E5%88%86%E9%A2%98%E7%9B%AE%EF%BC%89)
属于0/0型 采用罗比塔法则
原式= lim(x-0) [ tan(sinx)*cosx] / [sin(tanx)* 1/cosx^2]
换算等价无穷小有:
=lim(x-0) [ tan(sinx)*cosx] / [sin(tanx)* 1/cosx^2]
换算等价无穷小有:
=lim(x-0) [ sinx*cosx] / [tanx*1/cosx^2]
=lim(x-0) [ sinx*cosx^2] / [sinx]
=cosx^2|x=0
=1
原式= lim(x-0) [ tan(sinx)*cosx] / [sin(tanx)* 1/cosx^2]
换算等价无穷小有:
=lim(x-0) [ tan(sinx)*cosx] / [sin(tanx)* 1/cosx^2]
换算等价无穷小有:
=lim(x-0) [ sinx*cosx] / [tanx*1/cosx^2]
=lim(x-0) [ sinx*cosx^2] / [sinx]
=cosx^2|x=0
=1