MethodMath Math Questions and Answers

I am studying graph theory and I keep confusing Eulerian paths with Hamiltonian paths. Can someone clarify the difference?

Eulerian path: A path that uses every edge exactly once.
**Hamiltonian

I have a trig final next week and Im drowning in identities.

Theres like 50 of them:

• Pythagorean identities
• Angle addition formulas
• Double angle formulas
• Half

This is an IIT-JEE problem that has been bothering me:

Find the number of solutions to the equation $\sin x = \frac{x}{10}$ for $x \in \mathbb{R}$.

I tried solving it analytically but it seems

I understand that factorial means multiplying down:

and

But then I see this:

and it feels wrong.

If there are zero numbers to multiply, why is the

I'm in a calculus class and we proved that $\frac{d}{dx} \sin x = \cos x$ using the limit definition of the derivative:

But the proof uses the identity $\sin(A+B) = \sin A \cos B + \cos A \sin B$ and then relies on two

I'm preparing for IIT-JEE and I need to understand the classic proof that $\sqrt{2}$ is irrational. I've seen the proof but I have some doubts about the logic.

The proof

Consider the Diophantine equation

where $p$ is a prime and we seek non-trivial integer solutions $(x,y,z) \in \mathbb{Z}^3 \setminus \{(0,0,0)\}$.

By a classical descent argument using the fact that $\mathbb{Q}(\sqrt{-3})$ has class

In school they told us "you cant divide by zero" but they never explained WHY.

Like if you divide a number by a really small number you get a really