$\ln(x^2)$ vs $2\ln x$
These two are supposed to be equivalent because of the properties of logarithms, but the domains of $\ln(x^2)$ and $2\ln x$ seem different to me. For exam...
Apr 22, 2026 1 VIEWS
Topic: General
5104 Articles 
Why does Ridders' method work as well as it does?
I've just read section 9.2.1 in Numerical Recipes Ed. 3 (Press et al. 2007), which describes Ridders' method of root finding. I understand that ...
Apr 22, 2026 1 VIEWS
probability of having 2 boys given at least 1 is a boy
I am in 12th grade and I can't really understand a question in conditional probability. The question states There is a family with 2 children either ...
Apr 22, 2026 1 VIEWS
To find two sides of a triangle when it is circumscribed a circle
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of...
Apr 22, 2026 1 VIEWS
Find $\int x^2\arcsin(2x)dx$
Find $\int x^2\arcsin(2x)dx$ My work. $\frac{1}{3}\int \arcsin(2x)dx^3=\frac{1}{3}(x^3\arcsin(2x)dx-\int x^3d(\arcsin(2x))$ This yields to finding $\int \...
Apr 22, 2026 1 VIEWS
Trigonometry help
Taking online classes and trying to find the angle in degrees of csc when given a decimal Example in text not helping Question is csc (theta) = 1.245 and ...
Apr 22, 2026 2 VIEWS
First Order Approximation Taylor Series
I have the taylor series $f(z)=f(x_0)+(x-x_0)f'(z)+1/2(x-x_0)^2f''(z) ...$ and I am told that "As a first order approximation," $x-x_0$ ~ $...
Apr 22, 2026 1 VIEWS
Why are the hyperbolic functions defined the way they are?
I know that $\sinh(x) := \frac{e^x-e^{-x}}{2}$ and $\cosh(x) := \frac{e^x + e^{-x}}{2}$ by definition. But what exactly is the significance of this and ho...
Apr 21, 2026 1 VIEWS
How can I use Euler's Method in order to find the value of a constant k given the differential equation?
So, I am trying to attempt part b of this problem using my answer from part a. I just want to confirm if I did part a correctly and how I can do part b?
Apr 21, 2026 1 VIEWS
How do I convert an Arctangent into degrees by hand?
If I have $\arcsin(8/20)$, what angle is this? This is from Wikipedia and the answer is $21.8^{\circ}$. But I do not understand, by hand, how I can get th...
Apr 21, 2026 1 VIEWS
A closed Knight's Tour does not exist on some chessboards
It is generally difficult to determine whether a (large) graph have no Hamilton cycle (As opposed to determining whether it has any Euler circuit). This e...
Apr 21, 2026 1 VIEWS
Prove that $\exp(x)>0$ using only formal definition of exp
This problem would be easy if I could use the fact that $\exp(x)=e^x$, but I have to use the following definition: $$\exp(x)=\sum_{n=0}^{\infty}\frac{x^n}...
Apr 21, 2026 1 VIEWS