Calculator/Math Thread

**ben1996123** · 03-04-2012

I'm bored. Someone give me a random derivative to do please. No weird functions like Li(x), x!, W(x).

**tozies24** · 03-04-2012

Originally Posted by ben1996123

I'm bored. Someone give me a random derivative to do please. No weird functions like Li(x), x!, W(x).

x*sinx*e^x*lnx*cosx

**blah** · 03-04-2012

Originally Posted by Hyrtsi

I love maths. I've been doing research on my own on various problems and theorems, even came up with something on my own.

I'd like to see different ways to solve this:

Proof that

Originally Posted by y235

It's pretty easy.

Spoiler:

Originally Posted by Sa967St

Spoiler:

assumed convergence fail?

$x = 1 - 1 + 1 - 1 + \cdots \Rightarrow x = 1 - x \Rightarrow x = \frac12 \Rightarrow \text{lololololol}$

moral of the story: you can't just "set some infinite thingy equal to x" without first proving that such an x exists

**vcuber13** · 03-04-2012

how do you get that?

**AustinReed** · 03-04-2012

Hardest for me was basic algebra. Why? I had the teacher that couldn't teach. I suck at math because of him.

**ben1996123** · 03-05-2012

'Extended' product rule:

If $y = f(x)g(x)h(x)\cdots$ with n functions, and where n(x) is the nth function, $\frac{dy}{dx}=\sum_{r=1}^{n}\frac{r'(x)y}{r(x)}$ . It's probably known, but I found it myself today so I thought I'd post it.

Originally Posted by tozies24

Spoiler:

$\frac{dy}{dx}=e^x(sin(x)cos(x)ln(x)+xcos^2(x)ln(x)+xsin(x)ln(x)cos(x)$

Here's a derivative for someone to do:

$x^{sinh(x+y)}=\frac{2^{ln(xy)}}{y^{csc(x)}}$

Hint: $\frac{d}{dx}(sinh(x))=cosh(x), \frac{d}{dx}(cosh(x))=sinh(x)$

**samehsameh** · 03-05-2012

Pretty good example ben its all simple calculus just lots and lots of it. Will post a solution tomorrow, its 2:54 am atm and ive got lectures tomorrow morning, been teaching some friends how to cube

Also someone can try $\int_{-\infty}^{\infty} \! \frac{x\sin x}{x^2+a^2} \, \mathrm{d} x, a > 0$ i.e. the area enclosed by $y=\frac{x\sin x}{x^2+a^2}$ and

**Sahid Velji** · 03-05-2012

Twenty people are to travel in a bus from the airport to the hotel at the resort. The bus is designed for use in a tropical climate; it can carry twelve passengers outside and eight inside. If four of the passengers refuse to travel outside and five will not travel inside, in how many ways can the passengers be seated if the combinations of passengers inside or outside is not considered except to take into account these wishes?

Answer:

Spoiler:

**RussianWhiteBoi** · 03-05-2012

How can a branch of math be the "hardest" if everything connects to each other? It's like you have a million puzzles pieces, and just as you learn a new branch of math you manage to put together a hundred pieces.... only to find out a thousand more are missing. What's difficult for someone depends on which puzzle pieces are already assembled.

Spoiler:

**Sa967St** · 03-05-2012

Originally Posted by Sahid Velji

Twenty people are to travel in a bus from the airport to the hotel at the resort. The bus is designed for use in a tropical climate; it can carry twelve passengers outside and eight inside. If four of the passengers refuse to travel outside and five will not travel inside, in how many ways can the passengers be seated if the combinations of passengers inside or outside is not considered except to take into account these wishes?

Answer:

Spoiler:

The answer seems low, and it's not even close to what I thought it was.