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Since this is homework, I am not allowed to post the problem, so I will describe it in more general terms.

In a store there are N types of objects. Each object has a price and a list of compatible...

I have a relationship for about 10 months with a guy and the last two months have been at the distance. In two weeks I will celebrate my birthday and I overheard he wanted to make me a surprise....

Oh, that's easy, it's zero. Thank you!

I kind of stumbled on these 3 limits. I tried to solve 2 of them, but I don't know if it's correct and for the third one I don't have any idea where to start from. Could help me, please?

1. ...

1*1! + 2*2! + 3*3! +... +n*n! And how do you get it?

I've been with my boyfriend for 6 months now and he has always been a liar. I didn't care much when we first met because I didn't know I was going to have a relationship with him later and his lies...

I don't want to be rude, but it does sound like a movie script. I'm not sure if your story really happened this way or it is you that see it this way. Never mind. Judging by what you said it's easy...

10 days ago I lost my virginity but we didn't really have sex. It was just a trial to get myself accustomed to it (I needed patience to get rid of some bad memories related to sex) and I accepted to...

I've always had faith in God but I still can't understand why people have to die...

That my father is sick and he could die soon.

I'm sorry to add that it was not my concern after her death. She died 8 years ago, I never met her, so when I entered her house for the first time it was like a museum for me. Please, do no...

Actually, there are a lot of things going on in my life: I work in shop a couple of hours a day, I read a lot, I hang out with friends, go to the gym etc. I don't have time to get bored or worry...

The question is: how can I change my view towards death?

I'm sorry for your loss and for "offending" death, but this is how I feel, it's not my choice to feel this way.

I'm not afraid of dying, but I'm terrified when thinking that one day my parents will die, my friends, my future husband etc. Even if I wasn't close to a person, but I knew him/her while they were...

I've tried watching Prison Break, Covert Affairs, Supernatural, Suits, Lie to me, Sherlock Holmes, Lost, Nikita, One Three Hill, Awake, The Game of Thrones, Merlin, House, Six feet under, The...

Thank you, Ebaines! I did work out, indeed! :)

(\sin x + \cos x)^2 = \sin^2 x + \cos^2 x + 2 \sin x \cos x

\Rightarrow \sin x \cos x = \frac{(\sin x + \cos x)^2 -1 }{2}

\cos \(x -...

I need to bring this equation \sin x + \cos x - \sin x \cos x - m = 0

to this form: 2 \cos^2 \( x - \frac{\pi}{4} \) - 2 \sqrt{2} \cos \( x - \frac{\pi}{4} \) +2m -1 = 000

How do I get...

Hey, amillersong! What you're feeling right now it's PERFECTLY NORMAL. I mean, you had a two years relationship with her and according to what you said, you had also been quite committed to her, so...

f : [0,2] \rightarrow R , f differentiable on [0,2] and f(0) = 0

Prove that \exists c \epsilon (0,2) so that f'(c) = \frac{f(c)}{2-c} is true.

2x^3 - 5x^2 + 20x - 9 = 0

x^3 - 3x + 2 = 0

That's a wonderful suggestion, tkrussell!

Oh, thank you, ksak2011! I didn't know about any of the songs you cited, but I enjoy them fully!

Today I caught him lying. I called him around 2 PM just to see what's new. I didn't have the time to call him when he wanted me to because I was at school, so I called him after classes. He didn't...

Oh, sorry, there should have been "+" between all the terms, but it seems there is a problem with the code.

So, the first equation should have been 28 = sqrt (a + b) and the second one 40 = sqrt (...

\left\{
\begin{array}{l l}
28=sqrt{a b}\\
40=sqrt{(20 a)^2 b^2}\\
\end{array} \right.

You're so right, Cat1864. You really alarmed me with this: I couldn't stand hearing this from him, so I must fix this problem as soon as possible.

I'm not sure if I let the impression that I'm...

I'm 19, he's 20.

We've constantly met in person about 2 weeks, every time in completely different situations, so I had the chance to learn how he is like around other people and only around me....

Thank you, imfkdup!
This is an extremely enlightening answer, I will follow your advice.

I have a long distance relationship with this guy I can hardly resist. I mean, he so mysterious, so funny and imaginative... still I usually don't know what he feels and how to comfort him in bad...

I'm not sure how to deal with this type of exercises. Here is what I solved so far:

1.
f(x)=f(x^2), x \geq 0
f(x)=f(x^2)=f(x^4)=...=f(x^{2n})
f(x)=f(x^{2n})\Rightarrow f(x)= \lim_{n \to...

Could you suggest me, please, some artists that have great songs (that both sound good and have meaningful lyrics) ? It doesn't matter what kind of music they play, I'm just looking for some songs...

How to approach this exercise? I've tried a lot of methods and always reached 0/0.

\lim_{x \to 0} \frac{\sin x - \tg x}{\sin^2 x \tg x }

Well, I don't quite understand your explanation for I haven't learned about derivatives yet, that's why I tried to use the formula \lim_{x \to 0} \frac{sin x}{x} = 1 , but at the numerator there is ...

\lim_{x \to 0} \frac {\cos 5x - \cos x}{\sin 4x} = \lim_{x \to 0} \frac{-2 \sin 3x \sin 2x}{\sin 4x} = \lim_{x \to 0} = \frac {-2 \frac {\sin 3x}{3x} \times 3x \times \frac {\sin 2x}{2x} \times 2x }{...

OK, thank you anyway.

Sorry, it is my fault I didn't mention that I'm looking for another method (e.g. summing lines / columns or other operations) so that I can calculate it easier.

Regarding the + I typed each of...

| -2a a+b a+c // b+a -2b b+c // c+a c+b -2c |

I have problems with displaying the "+" sign every time I post. Is there a specific rule for writing expressions containing "+" ?

\begin{vmatrix}
-2a & a+b & a+c \\
b+a & -2b & b+c \\
c+a & c+b & -2c
\end{vmatrix}

EDIT by Unknown008: Added the + signs.

For a mathematical display you should write math mathematical expression /math. "math" words must be between []

Thank you Corrigan. It is helpful, indeed, although I haven't learned about L'Hopital's rule yet.

I am getting started with the rest of the exercises, but I'm not sure about the those with both a...

... and \lim_{n \to \infty}

Sorry, there are some mistakes. It seems there occurred an error with "+".

1. lim [a + bn/(n^2 - 1)]^n = e^2

2. lim [(n^2 + an + 1)/(n^2 + 3n - 2)]^n = e

3. lim [(an^2 + bn + 2)/(bn^2 + 4n +...

Could you give me some advice on how to approach this type of problems, please?

a,b \epsilon R

1. \lim_{x \to \infty} \left(a \frac{bn}{n^2-1} \right)^n = e^2

2. \lim_{x \to \infty}...

Thanks a lot!

Thank you. I've been struggling to solve it for a few days, but now I'm so happy that I finally see the method. However, I didn't quite catch where you got the expressions from when n is odd / even.

There should have been A^{n+1} and (a_n) + (b_n) instead of (a_n)(b_n). I don't know what went wrong. :|

Given the matrix:
\[
A =
\begin{pmatrix}
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0
\end{pmatrix}
\]

Well, not really.

I haven't learnt about derivatives yet, so I guess the curve will help more.

In this case, I can deal with it, I just didn't know this exercise required some other knowledge....

How to calculate the minimum and the maximum value of the function f(x) = 3 cos3x - 4 sin3x - 2 ?