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Jul
14
comment help with funky function definition
Have you tried some examples?
Jul
7
comment Determine $x$ coefficient of $f(x)=( (x+1/x)^a+(x-1/x)^a)^b$
If you redistribute the $x^{ab}$ inside the bracket, then all your exponents are positive. Beyond that, I can't see a clever trick that's better than the multinomial formula.
Jul
4
awarded  Enlightened
Jul
3
answered Determine $x$ coefficient of $f(x)=( (x+1/x)^a+(x-1/x)^a)^b$
Jul
2
awarded  Curious
Jul
1
awarded  Nice Answer
Jun
30
answered Meaning of math symbol ~
Jun
30
answered How to find the exponent $z$ of $(-1)^z$ for a patterned series of signed ones?
Jun
29
comment Open Problems for High School Students
That's almost certainly not going to happen, but if it were then one of your best starting points is probably the answer I linked. If you want a project, pick an area (for instance, you mention graph theory) and pick up a textbook. If you can't understand it, work out what you're missing and fix it. Eventually (and this will take a very long time) you might hit something new.
Jun
29
comment Open Problems for High School Students
If by 'research' you mean solve an open problem, this is very unlikely. On the other hand, there are many open problems that you would be able to understand and gain some insight for very easily here
Jun
29
comment Finding the best possible $\delta$ for a continuous function.
Not quite $|a-x|<\delta$ means $-\delta<a-x<\delta$, which rearranges to $a-\delta<x<a+\delta$. This is the same as $|x-a|<\delta$, as we should expect.
Jun
28
answered Finding the best possible $\delta$ for a continuous function.
Jun
28
answered How to solve: $0 = -\sin \space 3x \cdot3, \left({\pi\over 12}, {7\pi \over12}\right)$
Jun
25
answered Is it true that “there is no such thing as the square root of minus one”?
Jun
25
answered Lies, damned lies, and statistics
Jun
25
answered Is 2+2 always 4?
Jun
25
comment Does a continuous probability density function (pdf) have zero values on +infinity and -infinity?
Is $f$ continuous?
Jun
23
comment the next square number is $(? )^2 = a_{1}a_{2}\cdots $ where $a_{i}$ is consecutive positive integer
Are you asking for square numbers, all of whose digits are consecutive (but these can be in any order)? Do you allow one-digit squares? Presumably you do not allow repetitions, so there are no such squares $\ge 10^{10}$ (so you can stop looking for $a$ at $10^{5}$).
Jun
23
awarded  Nice Answer
Jun
20
answered Convergence proofs: why is it necessary to prove specifically for $\epsilon$?