Value of $\sin^{-1}(\sin 10)$
For the past few hours, I have been trying to find out the value of the following term: $$\sin^{-1}(\sin 10) $$ I understand that the answer will not be $...
20 Apr 2026 1 READS
Archive: General
How to find the value of $c$ using the mean value theorem?
So I'm doing Mean Value theorem homework which states $$f'(c)=\frac{f(b)-f(a)}{b-a}$$ I have $f(x)=e^{\frac{-x}{2}}$ over the interal [0,12]. Us...
20 Apr 2026 1 READS
Does the limit exist?
I had a question about the definition of a limit. I know for a limit to exist the right hand limit must equal the left hand limit but what if the graph of...
20 Apr 2026 1 READS
find the general solution to the following homogeneous differential equation.
$$100\frac{dy^2}{dx^2} + y = 0$$ Is this worked out by using the auxillary equation such that: $$100m^2 + 1 = 0$$ so $m = \pm i\sqrt{1/100}$ ? So the gene...
20 Apr 2026 1 READS
complex and real spectral theorem for matrices
I am studying the spectral theorem for matrices, and the book says that if a $nxn$ matrix A is real and symmetric then its diagonalizable over $\mathbb{R}...
20 Apr 2026 1 READS
What exactly is the difference between a derivative and a total derivative?
I am not too grounded in differentiation but today, I was posed with a supposedly easy question $w = f(x,y) = x^2 + y^2$ where $x = r\sin\theta $ and $y =...
20 Apr 2026 1 READS
Fourier series and Fourier transform. Amplitude spectrum vs. Frequency spectrum
I would like to know if there are any differences between amplitude spectrum and frequency spectrum. Is there any link between these two notions?
20 Apr 2026 1 READS
Use the Shell Method to find the volume by revolving around the x-axis.
The functions are $x=\frac{y^2}{2}$, $x=2$, and $y=2$. I graphed it and it looks like the intersection points are $(2,2)$ and $(0,2)$. But I don't kn...
20 Apr 2026 1 READS
Fourier cosine and sine transforms of 1
What is the Fourier sine and cosine transform of $f(x)=1$? I have seen some sources refer to the transform of $f=1$ involving the Dirac Delta function, bu...
20 Apr 2026 1 READS
Find the volume of triangular pyramid
I have a plane, $x+2y+3z=12$ with $x$-intercept of $12$, $y=6$, and $z=4$. So between origin and these points, I have a pyramid. $(0,0,0)$, $(12,0,0)$, $(...
20 Apr 2026 1 READS
