7.19.2 Greatest hits from previous weeks

7.19.2.1 What is the equation to plot a vertical line?
7.19.2.2 How do I identify the source of a "Tag times protected" error?
7.19.2.3 How can I draw the Olympic rings with Mathematica?
7.19.2.4 What does # mean in Mathematica?
7.19.2.5 Finding Limits in several variables
7.19.2.6 How to calculate contour integrals with Mathematica?
7.19.2.7 How to manipulate 2D plots?
7.19.2.1 What is the equation to plot a vertical line?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=59476

Please help. Trying to find area between three curves,  e^-x, x = 2, y = 1 . Can't find out how to plot  x = 2 . Don't want to use <... 
[plotting] [calculus-and-analysis]
 
asked by Cory https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=19717 6 votes
7.19.2.2 How do I identify the source of a "Tag times protected" error?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=11982

I have some code that looks like 
 
 Table[ 
a = 1; 
b = {2, 3} 
c = i;, 
{i, 2} 
] 
 
 
which gives an error: 
Set::write: Tag Times in c {2,3} is Protected.... 
[warning-messages] [syntax] [debugging] [faq]
 
asked by dearN https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=204 30 votes
answered by Mr.Wizard https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=121 36 votes
7.19.2.3 How can I draw the Olympic rings with Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=8885

How can I draw the 5 interlocking Olympic rings with Mathematica? 
(SVG version) 
Edit 
 
Hard choice, but some pretty cool answers here. I didn't have 3D answers in mind when I posted the question, but ... 
[graphics] [generative-art]
 
asked by Mike Honeychurch https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=77 44 votes
answered by cormullion https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=61 23 votes
7.19.2.4 What does # mean in Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=19035

I asked Mathematica to compute the following 
 
 Solve[c (1-x)^2-x^(1/4) == 0, x] 
 
 
and it returned this: 
x = Root[#1^8 c^4 - 8 #1^7 c^4 + 28 #1^6 c^4 - 56 #1^5 c^4 ... 
[syntax] [core-language]
 
asked by ronanymous https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5730 43 votes
answered by Dr. belisarius https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=193 71 votes
7.19.2.5 Finding Limits in several variables

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=21544

Is there a way to find a limit of a multivariable function, like 
 
$$\lim_{(x,y)\to (0,0)} f(x,y)$$ 
with Mathematica? 
 
When $f$ is continuous, we can use 
$$\lim_{(x,y)\to (0,0)} f(x,y)=\lim_{(x,0)\... 
[functions] [calculus-and-analysis]
 
asked by Dominic Michaelis https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5899 31 votes
answered by whuber https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=91 42 votes
7.19.2.6 How to calculate contour integrals with Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=34073

How to calculate the integral of $\frac{1}{\sqrt{4 z^2 + 4 z + 3}}$ over the unit circle counterclockwise for each branch of the integrand? 
[calculus-and-analysis] [complex]
 
asked by user64494 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=7152 42 votes
answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 64 votes
7.19.2.7 How to manipulate 2D plots?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=7142

When it comes to visual analysis, large datasets or data with intricate internal details often makes plotting in 2D useless, as the outcome is either just a fraction of the full dataset, or no details ... 
[plotting] [graphics] [dynamic] [gui-construction]
 
asked by István Zachar https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=89 137 votes
answered by István Zachar https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=89 155 votes