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 Sep11 comment Why does $x^{(1/\ln(x))} = e$? Take the natural log of both sides and insight is not far off. Jun12 comment Curve fitting to connect certain points What is the significance of the blue curve? Why are the interpolation points represented as triangles? How do they affect/constrain the black curve? May22 comment How to calculate per unit costs for multiple items Does 'x' represent a variable or multiplication? May22 comment Time-varying frequency waveform A couple of things to consider. First you should make sure that the requested frequency is no more than 1/2 of the signal sample frequency to avoid aliasing. Second, what you are trying to do here is frequency modulation. If you read the Wikipedia article, you will see that it generates higher frequencies than expected. Third, depending on how the wave is synthesized, you need to adjust the phase of the signal to make sure it is continuous. I am not sure if your method does that. May19 comment Laplace transform of unit step function By definition: $f(t) = \begin{cases} t, & \text{$0 \le t \le 1 $} \\ 0, & \text{$1 \lt t \lt \infty$} \\ \end{cases}$ May19 comment Laplace transform of unit step function The function is zero for $t>1$. You don't need to integrate it. May19 answered Laplace transform of unit step function May19 comment Laplace transform of unit step function Can you use a Laplace transform table? The function above is only useful if you are using a table. Otherwise just integrate from 0 to 1, i.e. $F(s)= \int_0^1e^{-st}tdt$. May19 comment Laplace transform of unit step function The function you want to use is $f(t)=t(u(t)-u(t-1))$. May14 comment Gaining Linear Algebra Intuition — Subspaces This set of lectures helped me a lot: ocw.mit.edu/courses/mathematics/…. May14 revised Gaining Linear Algebra Intuition — Subspaces Thought this tag may help clarify OP intent. May7 comment Show that exist a rotation $r$ such that $r(u)=v$ Hint: You need the axis-angle representation of a rotation (see: en.wikipedia.org/wiki/Axis_angle). You can use the dot product to find the angle and the cross product to find the axis. Mar11 reviewed Approve Double Angle Formula? Mar8 reviewed No Action Needed What are the odds of a specific 5 digit combination appearing within an 8 digit combination of numbers in any order/any recurrences from 0-9. Mar8 reviewed Approve Why does the following nonlinear system have 21 solutions? Mar8 reviewed Approve Is the function $f(x,y) = \sin(\frac{r}{\theta}), f(0,0) = 0$ continous at the point $(0,0)$? Feb27 reviewed Approve Let $T$ be a tree of order $n$. Why is the complement $\neg T$ of $T$ the same size as $K_{n-1}$? Feb26 comment Are orthogonal spaces exhaustive, i.e. is every vector in either the column space or its orthogonal complement? @Ethan, Yes, you are correct that the union (in the formal sense) between the two subspaces is zero. I took the sense of your question at the end of the first paragraph "are there some vectors in $R^n$ which are in neither?" I thought that by using the term union, you intended span. Feb26 comment Are orthogonal spaces exhaustive, i.e. is every vector in either the column space or its orthogonal complement? Feb25 comment How To Generate Random Points on the Positive Side of a Plane in 3-D See my second edit.