1.lim(x→0)[(1/x^2)-(1/xsinx)] 2.lim(x→0) [(1/e^x -1)-(1/x)]
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1.lim(x→0)[(1/x^2)-(1/xsinx)] 2.lim(x→0) [(1/e^x -1)-(1/x)] 3.lim(x→0) [(1/x-1)-(2/x^2 -1)]
4.f'(x)=k,求 lim(x→0)[(f(x0+2x)-f(x0-x))/x] 5.f(x)={x^3sin(1/x),x不等于0,0,x=0 ,则f'(0)=?6.y=3^x,求y^(100)(0) 7.y=x^2arctanx,求dy,y'',8.y=(x+1)e^((x^2)+1),求dy,y''
4.f'(x)=k,求 lim(x→0)[(f(x0+2x)-f(x0-x))/x] 5.f(x)={x^3sin(1/x),x不等于0,0,x=0 ,则f'(0)=?6.y=3^x,求y^(100)(0) 7.y=x^2arctanx,求dy,y'',8.y=(x+1)e^((x^2)+1),求dy,y''
![1.lim(x→0)[(1/x^2)-(1/xsinx)] 2.lim(x→0) [(1/e^x -1)-(1/x)]](/uploads/image/z/2378322-18-2.jpg?t=1.lim%28x%E2%86%920%EF%BC%89%5B%281%2Fx%5E2%29-%281%2Fxsinx%29%5D+2.lim%28x%E2%86%920%29+%5B%281%2Fe%5Ex+-1%29-%281%2Fx%29%5D)
题目太多了,没人做滴的.我来选1个做一下:
lim(x→0)[(1/x^2)-(1/xsinx)]
1/x^2-1/xsinx =(sinx-x)/x^2*sinx
分子分母求导数 (cosx-1)/(2xsinx+x^2*cosx)
还是0/0型,再一次分子分母求导数
-sinx/(2sinx+2xcosx+2xcosx-x^2*sinx)
再求导
-cosx/(2cosx+4cosx-4xsinx-2xsinx-x^2*cosx)
x→0
=-1/(2+4)
=-1/6
lim(x→0)[(1/x^2)-(1/xsinx)]
1/x^2-1/xsinx =(sinx-x)/x^2*sinx
分子分母求导数 (cosx-1)/(2xsinx+x^2*cosx)
还是0/0型,再一次分子分母求导数
-sinx/(2sinx+2xcosx+2xcosx-x^2*sinx)
再求导
-cosx/(2cosx+4cosx-4xsinx-2xsinx-x^2*cosx)
x→0
=-1/(2+4)
=-1/6
1.lim(x→0)[(1/x^2)-(1/xsinx)] 2.lim(x→0) [(1/e^x -1)-(1/x)]
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lim(x→0)x/(xsinx)=0和lim(x→0)(xsinx)/x=1
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求极限lim[e^xsinx-x(1+x)]/x^3 其中X趋向于0
lim(x~无穷)xsin1/x-1/xsinx
lim(x→0)(1-cosx)/(xsinx)=?