6.22.2 Greatest hits from previous weeks

6.22.2.1 Assign the results from a Solve to variable(s)

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=6669

I understand Mathematica can't assign the results of a Solve to the unknowns because there may be more than 1 solution. How can I assign the 4 values of following result to variables? 
... 
[equation-solving] [assignment] [faq]
 

asked by stevenvh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1450 56 votes

answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 34 votes

6.22.2.2 Finding unit tangent, normal, and binormal vectors for a given r(t)

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=18598

For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$. 
 
I've got Mathematica, but I've never used it before and I'm not sure how to coerce ... 
[equation-solving] [calculus-and-analysis] [geometry] [vector-calculus] [homework]
 

asked by a98 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5605 30 votes

answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 43 votes

6.22.2.3 Multivariable Taylor expansion does not work as expected

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=15023

The basic multivariable Taylor expansion formula around a point is as follows: 
 
$$ 
f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot \nabla)... 
[calculus-and-analysis] [series-expansion]
 

asked by matheorem https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4742 58 votes

answered by Jens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=245 65 votes

6.22.2.4 xkcd-style Plots

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=11350

I received an email to which I wanted to respond with a xkcd-style graph, but I couldn't manage it. Everything I drew looked perfect, and I don't have enough command over ... 
[plotting] [generative-art]
 

asked by Amatya https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=2039 615 votes

answered by Simon Woods https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=862 474 votes

6.22.2.5 What's the most difficult multidimensional integral that Mathematica has solved?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=222184

I am interested in benchmarking numerical integration methods and am trying to develop a wider set of difficult multivariate examples. For my particular methods, I only want to look at non-negative-... 
[calculus-and-analysis] [numerical-integration]
 

asked by ben18785 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=19278 6 votes

6.22.2.6 Drawing a square root spiral

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=66969

Here is a start. I'm looking for a nice way to draw it. 
 
... 
[graphics] [geometry]
 

asked by matrix89 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5379 24 votes

answered by Bob Hanlon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=9362 21 votes

6.22.2.7 Get a "step-by-step" evaluation in Mathematica

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=148

Is it possible in Mathematica to get a step-by-step evaluation of some functions; that's to say, outputting not only the result but all the stages that have led to it? If so, how does one do it? 
 
... 
[evaluation] [interactive] [faq]
 

asked by Cydonia7 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=44 125 votes

answered by J. M.'s discontentment https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=50 105 votes