The task is as follows: Given: $$F(x,y,z) = 0$$ Goal: Show $\frac{\partial z}{\partial y}|_x \frac{\partial y}{\partial x}|_z \frac{\partial x}{\partial z...

Why should the gradient be $0$ at a critical point? I'm not sure the reason other then we set the gradient of a function to zero to find the critical...

Question: https://gyazo.com/acce090bee3f6ccc8346b39e2fe5ab4b My solution and to the part where I do not understand: https://gyazo.com/72ab1498de0455f79a04...

Suppose that $R$ is a non-commutative unital ring and $M$ is a two-sided maximal ideal of $R$. What can we say about $R/M$? How close can we get to the an...

Evaluate the line integral $$\int_C (x+2y)dx + x^2dy,$$ where $C$ consists of line segments from $(0,0)$ to $(2,1)$ and from $(2,1)$ to $(3,0)$. How do yo...

I found an online blackjack that has no minimum or maximum bet limit. The dealer stands on soft 17. Also, in the event that both dealer and player gets bl...

The title says it all, let's take this simple example: I want to find $c$. Using $\sin$ I get: $\sin(30)$ = $4 / c$ $c = 4 / \sin(30) = 8$ Now, using...

I am having trouble with a coordinate geometry question: Triangle ABC has been reflected. The pre-image has vertices at A(2, -1), B(4, 0), and C(3, -3). T...

It might be a silly question, but to me it is not obvious why the following expression holds: $$ \lim\limits_{x\rightarrow 0}\frac{0}{x}=0 ? $$

The solution to the equation (-2/k)*-4=-1 (k= -8) is a negative in the denominator. Is that allowed? thanks enter image description here