※ 引述《iverson32 (iverson32)》之銘言：
: 1.lim (1-3/x+6/x^2)^x
: x->無窮大
: 2.Find the tangent plane to the surface sin(x+y+z)=xyz at pt.(1.-1.0)
: 3.The 3rd-degree Taylor polynomial of f(x)=sin(e^x^2-1) about 0 is
: 4.A wedge is cut of a circular cylinder of radius 6 by two planes.One plane is
: perpendicular to the axis of the cylinder.The other intersects the first at
: an angle of 45度 along adiameter of the cylinder.Find the volume of the wedge
1.令 y = 1/x , 則當 x→∞ 時 , y→0
lim (1 - 3/x + 6/(x^2))^x
x→∞
= lim (1 - 3y + (6)(y^2))^(1/y)
y→0
= lim e^((ln((1 - 3y + (6)(y^2))^(1/y))))
y→0
= e^(lim ln((1 - 3y + (6)(y^2))^(1/y)))
y→0
ln(1 - 3y + (6)(y^2))
= e^(lim -----------------------)
y→0 y
(-3 + 12y)/(1 - 3y + (6)(y^2))
= e^(lim --------------------------------)
y→0 1
-3 + 12y
= e^(lim -------------------) = e^(-3)
y→0 1 - 3y + (6)(y^2)
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