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Interval Notation for the set of real numbers
So basically, interval notation has 4 basic forms 1) $\{1,2,3,4\}$ with example: the set of natural number $N=\{1,2,3,4,5,6,7,8,9\}$ 2) $(a,b)$ 3) $[a,b)$...
Apr 22, 2026
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How to expand this polynomial division?
My Physics teacher gave me a problem and its solution, what I have todo is to expand the solution, but when I do it I do not get to the same solution he s...
Apr 22, 2026
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Volume of solid of revolution about y-axis
I need to find the volume of a solid of revolution formed by rotating the region bounded by these curves: $y=4+x^2,$ $x=0,$ $y=4+x^2,$ and $x=1$ about the...
Apr 22, 2026
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Is there a function with a removable discontinuity at every point?
If memory serves, ten years ago to the week (or so), I taught first semester freshman calculus for the first time. As many calculus instructors do, I deci...
Apr 22, 2026
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Prerequisites for Studying a Book on PDE's
I'm taking a course on Electromagnetism that will cover the boundary-value problems -- the solutions to Laplace's and Poisson's equations f...
Apr 22, 2026
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Perfect Set and Compact Set
I am having some difficulty in understanding the difference between Perfect and Compact sets. More specifically, my problem is rather understanding how Pe...
Apr 22, 2026
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Evaluating the line integral
The question I'm working on states: Let $C$ be the curve in $\mathbb R$ consisting of line segments from $(4,1)$ to $(4,3)$ to $(1,3)$ to $(1,1)$. Le...
Apr 22, 2026
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Estimate the volume of a shape using the trapezoidal rule.
A 100 foot tall tree trunk has a circular cross section at every height and its circumference is given by the following table. Estimate the volume of the ...
Apr 22, 2026
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How to solve $x^3=-1$?
How to solve $x^3=-1$? I got following: $x^3=-1$ $x=(-1)^{\frac{1}{3}}$ $x=\frac{(-1)^{\frac{1}{2}}}{(-1)^{\frac{1}{6}}}=\frac{i}{(-1)^{\frac{1}{6}}}$...
Apr 22, 2026
![solving $3x^2 +4x-2= 0\pmod{31}$ [duplicate]](https://news.conceivablytech.com/uploads/solving-3x-2-4x-2-0-pmod-31-duplicate_720.jpg)
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solving $3x^2 +4x-2= 0\pmod{31}$ [duplicate]
I tried multiplying both sided by 4a which leads to $(6x+4)^2=40 \pmod{372}$ now I'm stuck with how to find the square root of a modulo.
Apr 22, 2026
