The set of real numbers is a subset of the set of complex numbers?
So, I was taught that $\mathbb{Z}\subseteq\mathbb{Q}\subseteq\mathbb{R}$. But since the set of complex numbers is by definition $$\mathbb{C}=\{a+bi:a,b\in...
Published: Sep 06, 2026
Finding the Equation of the Ellipse By Completing the Square
I have the following equation of an ellipse: $$5x^2+9y^2+40x=100$$ I need to put it in the form: $$\frac{(x-h)^2}{m^2} + \frac{(y-k)^2}{n^2} =1 $$ I was t...
Published: Sep 06, 2026
How can i apply Absorption law in this expression?
I have this expression: A + A * B * C' I know that i can use the Absorption law in this and the answer is A, but how can i apply that? Thank you.
Published: Sep 06, 2026
why measure theory for probability?
I studied elementary probability theory. For that, density functions were enough. What is a practical necessity to develop measure theory? What is a probl...
Published: Sep 06, 2026
convergence of the series involving log function
I was asked about convergence of summation of $\log(n)/n^2$ and $\log(1+(1/n))/n^2$. I want to use only p series test. Is there any approximation for $\lo...
Published: Sep 06, 2026
Understanding a limiting procedure
Say I have a function $f(x,y)$ that is defined for all $x \leq 0$ except at a single point $x=x_0 \neq 0.$ There exists one representation of the function...
Published: Sep 06, 2026
Calculating deposit based on interest and required withdrawal in future
I am really stuck with example 2-5 and 2-6. I don't really understand example 2-6 and example 2-5 I just can't figure out...I was able to do exa...
Published: Sep 06, 2026
Two different notations for inner product
In my linear algebra course on the faculty of mathematics, we used the following notation for the inner product: $$\langle v, w \rangle$$ On the other han...
Published: Sep 06, 2026
Give a big-O estimate for a function f(x), use a simple function g of the smallest order.
Task Find a function $g(x)$ that is Big-O of $f(x)$ $f(x)$ is $\mathcal{O}(g(x))$ $f(x)=n\cdot log(n^2+1)+n^2\cdot log(n)$ I tried to follow/copy one of t...
Published: Sep 06, 2026
solve surface integral of a scalar function using divergence theorem
Use the Divergence Theorem to evaluate: $$\iint_S (2x+2y+z^2) dS$$ where $S$ is the sphere $$x^2+y^2+z^2=1.$$ Most of the examples on the book that needs ...
Published: Sep 06, 2026
