# Tagged Questions

For questions about parametric equations, their application, equivalence to other equation types and definition.

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### Evaluating the Surface Integral $\iint_{x^3+y^3+z^3=a^3} \frac{\bf{x}}{||\bf{x}||} \cdot d\bf{S}$

Compute the surface integral: $$\int_S({x\over \sqrt{x^2+y^2+z^2}}, {y\over \sqrt{ x^2+y^2+z^2}}, {z\over \sqrt{x^2+y^2+z^2}}) \cdot \vec n \ dS$$ where $S: x^3+y^3+z^3=a^3$ The first ...
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### What is parameterization?

I am struggling with the concept of parameterizing curves. I am not even sure if I know what it means so I tried to look some things up. On Wikipedia it says: Parametrization is... the process of ...
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### Find the length of the curve $x^{2k}+y^{2k} =1$

I want to find an expression for length and find the limit $k\rightarrow \infty$ The answer is obviously 8, if we look at the graphs.
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### Can (x(t), y(t)) generate a surface? If so, can the surface be continuous?

Intuitively, the parametric equation $z = (x(t), y(t))$ seems to only be able to generate one-dimensional objects, i.e. curves. However... Let $x(t)$ be "the odd-indexed digits of the real number $t$"...
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### Parametrizing a given line and equations

1) Parametrizethe given line contraining the points (3,2) and (-5,6). 2) Find the parametric equations for the segment joining the given points (2,3) and (5,5) where $0\leq t \leq 1$. 3) ...
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### What is the parametric equations for the following closed curves?

First case Second case For the sake of simplicity, let the circle of radius $R$ be at the origin, the rectangle width and height be $w$ and $h$, respectively.
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### Writing Polar Equations In Parametric Form

For an example problem, in my textbook, the author wanted to demonstrate how to graph a polar function. Deeming it most convenient, my author took the polar function $r=2\cos 3\theta$, and re-wrote it ...
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### Eliminate $t$ to give an equation that relates $x$ and $y$

I am having problems understanding how to solve the following parametric equation. I have achieved an answer, but am unsure if my answer is correct or not. Eliminate t to give an equation that ...
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### what is the parametric form for “mystery curve”?

Mystery curve found here looks like this : Was given by the complex formula : $$e^{it} – \frac{e^{6it}}{2} + i \frac{e^{-14it}}{3}$$ Is the parametric form simpler or the polar form would be ...
### Show three ways that $f(z)=\frac{\overline{z}}{z-1}$ is not analytic
I need to show the complex function $$f(z)=\frac{\overline{z}}{z-1}$$ is not analytic in three ways; using Cauchy's equations, geometrically, and by integrating over the circle of radius 2. I used ...
### All $a$ that equation has at least one root. $a^2+7|x+1|+5 \sqrt{x^2+2x+5}=2a+3|x-4a+1|$
Find all $a$ such that the equation has at least one root. $$a^2+7|x+1|+5 \sqrt{x^2+2x+5}=2a+3|x-4a+1|$$ What have I done: substitution $t=x+1$ and some rearrangements (a-1)^2-1+7|t|+5\sqrt{t^2+4}-3|...