For basic questions about limits, derivatives, integrals, and applications, mainly of one-variable functions.

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3
votes
1answer
242 views
+200

The root of summation function

This is a calculation I need for my statistics project Big edit: simplify the function $f(x)$ a lot. Define for $f(x)$, $x\geq 0$, $$ f(x):=\sum_{k=1}^\infty ...
3
votes
0answers
165 views
+50

How do find the numerical average of $x^x$ from $(-4,-2)$ without x-values that give a complex output?

I wanted to find the approximate average of all real points in $(x)^{x}$ from $[-4,-2]$. This means I am ignoring all real inputs that give a complex output and need average to be a real number. To ...
5
votes
1answer
135 views
+50

Is it to the students' advantage to learn the language of infinitesimals?

A colleague of mine asked an interesting question reproduced below with his permission. It is reasonable to ask whether it is to the students' advantage to learn the language of infinitesimals - ...
0
votes
1answer
33 views
+50

How to find centroid of this region bounded by surfaces

I am having difficulty find the centroid of the region that is bound by the surfaces $x^2+y^2+z^2-2az=0$ and $3x^2+3y^2-z^2=0$ (lying above $xy$ plane, consider the inner region). I know the first ...