lim[x²／x²-1﹚]^x
=lim[1+1/(x^2-1)]^x
=lim[1+1/(x^2-1)]^{(x^2-1)]*[x^2/(x^2-1)]}
=lim[1+1/(x^2-1)]^(x^2-1)]
=e(1)、證明：
∴A1B1=(-1,1,0) A1A=(0,0,√2) C1D=(1/2,1/2,0)
∴A1B1·C1D=0 A1A·C1D=0
∴A1B1⊥C1D A1A⊥C1D
又∵A1B1∈平面AA1B1B 且A1A∈平面AA1B1B 且A1A與A1B1不平行
∴C1D⊥平面AA1B1B
(2)、∵AB1=(-1,1,-√2)
∴AB1·C1D=0
∴AB1⊥C1D
∴只要AB1⊥DF時,就會有AB1⊥平面C1DF
又∵DF=(-1/2,1/2,z)
∴AB1·DF=1-z√2
∴當z=1/√2時,AB1⊥DF
即：F點坐標為(0,1,1/√2) 即BB1中點時,會使得AB1⊥平面C1DF