Hello!!! If we have the following: Find where the tangent plane of $z=e^{x-y}$ at $(1,1,1)$ intersects the z-axis.
we can find the tangent plane using the formula $z=f(x_0, y_0)+ \frac{\partial{f}}{\partial{x}} (x_0, y_0) (x-x_0)+\frac{\partial{f}}{\partial{y}} (x_0, y_0) (y-y_0) $
and then set $x=y=0$.
If we want to find where the tangent plane of $x^2+2y^2+3xz=10$ at $(1,2,\frac{1}{3})$ intersects the z-axis could we divide by 3x and solve for z and use the above formula?
I think not, because we would have to set x=0, but $z=\frac{10}{3x}-\frac{x}{3}-\frac{2y^2}{3x}$ does not hold fo…
I want to show that the dihedral group $D_n$ is nilpotent if ane only if $n=2^i$ for some $i$.
I have shown the direction $\Leftarrow$.
Could you give me some hints for the direction $\Rightarrow$ ?
We suppose that $D_n$ is nipotent and $n=2^im$, where $2\not\mid m$, or not?
How can we f...
