7.40.2 Greatest hits from previous weeks

7.40.2.1 Finding Limits in several variables
7.40.2.2 Smiley Face using parametric equations
7.40.2.3 Why I get the "Set::write: "Tag Times in is Protected." error?
7.40.2.4 Crack CAPTCHA using deep learning
7.40.2.5 How to add a vertical line to a plot
7.40.2.6 How to tell Mathematica that certain variables are real/imaginary, integer-valued, etc
7.40.2.7 How to graph a sphere with cartesian equations?
7.40.2.1 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 32 votes
answered by whuber https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=91 42 votes
7.40.2.2 Smiley Face using parametric equations

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=137669

I need to know the parametric equations for this smiley face and how to draw it in Mathematica.  I'm completely lost. 
[plotting] [parametric-functions] [homework]
 
asked by Woeseph https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=46575 1 vote
answered by Bob Hanlon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=9362 5 votes
7.40.2.3 Why I get the "Set::write: "Tag Times in is Protected." error?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=11868

Why I get the error below with this code: 
 
... 
[vector-calculus]
 
asked by Aurelius https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1669 10 votes
answered by Mark McClure https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=36 13 votes
7.40.2.4 Crack CAPTCHA using deep learning

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=143691

Deep convolutional neural networks are very good at computer vision related tasks. Optical Character Recognition (OCR) is one important branch of computer vision. In fact, the convolution neural ... 
[machine-learning] [neural-networks] [ocr]
 
asked by xslittlegrass https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1364 89 votes
answered by xslittlegrass https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1364 98 votes
7.40.2.5 How to add a vertical line to a plot

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=3561

In the plot below I would like to add two vertical lines at $x = \frac{\pi}{15} \pm \frac{1}{20}$. 
How can I do that? 
 
... 
[plotting]
 
asked by sjdh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=515 71 votes
answered by Ajasja https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=745 88 votes
7.40.2.6 How to tell Mathematica that certain variables are real/imaginary, integer-valued, etc

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=66273

I'm trying to expedite some quantum mechanical calculations (expectation values etc.) by running them through Mathematica. When I say, for example, 
... 
[functions] [complex] [assumptions] [variable-definitions]
 
asked by Matthew Brunetti https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=22304 45 votes
answered by SquareOne https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=19960 30 votes
7.40.2.7 How to graph a sphere with cartesian equations?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=24169

I'm new to Mathematica and I need to ask how to graph a sphere, cylinder, etc.. using cartesian equations. 
 
For example in sphere's case $x^2+y^2+z^2=1$ 
 
I tried to use ... 
[plotting]
 
asked by German https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=7145 8 votes
answered by Dr. belisarius https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=193 14 votes