Search found 151 matches

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

Re: Dhaka Higher Secondary 2011/10

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
by Avik Roy
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)...
by Avik Roy
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...
by Avik Roy
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...
by Avik Roy
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...
by Avik Roy
Tue Aug 30, 2011 9:00 pm
Forum: Social Lounge
Topic: Eid Mubarak!
Replies: 5
Views: 2099

Re: Eid Mubarak!

ঈদ মুবারক।
by Avik Roy
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 $f(x) = x^2$,...
by Avik Roy
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 :)
by Avik Roy
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.
by Avik Roy
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.
\[\lim_{n \to \infty}\frac {f(1) + f(2) + ... + f(n)} {n}\]