Ibrahim, it's expected that you use LATEX in this forum

And draw a diagram and you should have the explanation for why your answer is incorrect

## Search found 151 matches

- Sat Sep 03, 2011 10:34 pm
- Forum: H. Secondary: Solved
- Topic: Dhaka Higher Secondary 2011/10
- Replies:
**4** - Views:
**4482**

- Sat Sep 03, 2011 8:27 pm
- Forum: Algebra
- Topic: functional equation
- Replies:
**3** - Views:
**1530**

### Re: functional equation

I guess the following proof should hold. Lets consider the Mclaurin series expansion $f(x) = g_0 (x) + g_1 (x) + g_2 (x) + ... $ where $g_k (x) = a_k x^k$ Now, the left side of the equation (as written in earlier reply) demands that for all values of $k$ the following relation holds: \[\frac {g_k(x)...

- Sat Sep 03, 2011 7:59 pm
- Forum: Algebra
- Topic: functional equation
- Replies:
**3** - Views:
**1530**

### Re: functional equation

Rewriting the equation as \[ f'(x) = \frac {f(x) - f \left (\frac {x} {2} \right)} {\frac {x} {2}} \] This means that the straight line passing through $\left ( x, \frac {x} {2} \right )$ is the same as the slope of the function at $x$. This intuitively reveals that $f(x)$ is linear. For any pair of...

- Thu Sep 01, 2011 9:13 pm
- Forum: Algebra
- Topic: A Dirty Problem
- Replies:
**2** - Views:
**1176**

### A Dirty Problem

I came up with this problem myself. But I consider it to be a dirty one. Consider a function $f(x)$ to be defined from a subset $D$ of real numbers to the set of real numbers. $f(x)$ follows the following relation: \[f(x) = \frac {\lceil f(x) \rceil + \lceil x \rceil} {\lfloor f(x) \rfloor + \lfloor...

- Tue Aug 30, 2011 11:21 pm
- Forum: Higher Secondary Level
- Topic: Number Theory Problem
- Replies:
**4** - Views:
**2345**

### Re: Number Theory Problem

Quite late a reply, but a reply indeed. Prodip, you need to show how you obtained the solution. And also, you need to find the complete solution and must prove that there are none beyond what you show. In this case, the solutions are $162, 243, 324, 405, 605$ Lets rearrange the given equation as $10...

- Tue Aug 30, 2011 9:00 pm
- Forum: Social Lounge
- Topic: Eid Mubarak!
- Replies:
**5** - Views:
**2099**

### Re: Eid Mubarak!

ঈদ মুবারক।

- Tue Aug 30, 2011 8:57 pm
- Forum: Higher Secondary Level
- Topic: Differentiation
- Replies:
**17** - Views:
**5206**

### Re: Differentiation

The first question that tickles my mind: Can you actually define $x^2$ as a sum of $x$ number of $x$'s??? However, if yo keep insisting on relying on that definition, take it this way- The derivative of a function $f(x)$ approaches $\frac {f(x+h) - f(x)} {h}$ as $h \rightarrow 0$. When $f(x) = x^2$,...

- Fri Apr 01, 2011 1:24 pm
- Forum: Number Theory
- Topic: a problem
- Replies:
**9** - Views:
**3190**

### Re: a problem

Nice Problem. Giving a hint only-

Try with prime power factorization of $x$ and $y$. That'll lead you to some handy equations

Try with prime power factorization of $x$ and $y$. That'll lead you to some handy equations

- Wed Mar 30, 2011 4:17 pm
- Forum: Algebra
- Topic: probability
- Replies:
**1** - Views:
**955**

### Re: probability

One can't answer that unless the probability distribution function is known.

- Tue Mar 29, 2011 6:53 pm
- Forum: College / University Level
- Topic: average number of square sum representation
- Replies:
**2** - Views:
**3721**

### average number of square sum representation

Consider $f(n)$ to be the number of representations $n=x^2 + y^2$ for integral $x$ and $y$. Find the average number of such representations for a natural number, i.e.

\[\lim_{n \to \infty}\frac {f(1) + f(2) + ... + f(n)} {n}\]

\[\lim_{n \to \infty}\frac {f(1) + f(2) + ... + f(n)} {n}\]