11,457 reputation
21151
bio website math.rochester.edu/people/…
location Rochester, NY
age 25
visits member for 2 years, 4 months
seen 2 days ago

I'm a graduate student at the U of R in Rochester, NY. I enjoy recreational mathematics including problem solving and most things topology.


Jan
17
comment How do I evaluate $\int u^m (1-u^2)^n du$?
@M.S.E: $n$ may be very large indeed but always finite. We aren't taking any limits here, so $n$ is a fixed constant. Keep in mind this assumes $n$ is a positive integer (which seems plausible from the context, but it hasn't been stated).
Jan
16
comment Is it possible for it to be impossible to get to work on time?
In conjunction with Simon S, all you need to do is adjust the time you leave accordingly to force it to be impossible to arrive at work in time (I think any reasonable person will agree one who leaves at $8:59$am and works more than $1$ mile/kilometer away will not arrive at work on time under even the best of conditions).
Jan
15
revised Evaluating $\lim_{x\to0} \frac{(1+x)^{1/x}-e}{x}$
added 12 characters in body
Dec
31
comment Proving if an integral is positive, negative, or zero
Out of curiosity, what are you wanting to be more rigorous? The only part I can see that could be added is that the exponential term is decreasing since the derivative is negative, hence the integral in the latter interval is smaller.
Dec
31
revised Why are these two floor sequences equal?
added 100 characters in body
Dec
24
comment Properties of Derivative function on $\mathbb R[x]$
What have you tried?
Dec
22
revised Is it true that a continuous function with compact support is uniformly continuous?
corrected grammar
Dec
21
reviewed Close How to solve the differential equation $(2xy^2-y){dx}+(y^2+x+y){dy}=0$?
Dec
21
reviewed Close How can $ i $ be distinguished from $ - i $?
Dec
21
reviewed Leave Open Prove that if sets $A$ and $B$ are countable, then their union $A\cup B$ is countable
Dec
21
reviewed Close If $X\ge 0$ and $a\ge E[X]$, then $P(X\gt a)\ge (E(X)-a)^2/ E(X^2)$
Dec
20
awarded  Constituent
Dec
18
comment Want to ensure my proof is rigourous enough.
Remember your induction is on $n$, so if you know $r^n<1$, you want to show $r^{n+1}<1$ (hint: $r^{n+1}=r^n\cdot r^1$)
Dec
18
comment Lower bound for degree of polynomial.
+$1$ for answering the question of whether or not there is a lower bound.
Dec
18
comment Calculation of $\lim\limits_{x \to 0} \frac{\frac{\mathrm d}{\mathrm d x} (e^{\sec x})}{\frac{\mathrm d}{\mathrm d x} (e^{\sec 2x})}$
Just a note: if you look at the limit of the quotient of first derivatives, you can eliminate (or evaluate) everything except for $\tan(x)/\tan(2x)$. It simplifies the expression considerably when doing l'Hopital a second time.
Dec
18
comment Calculation of $\lim\limits_{x \to 0} \frac{\frac{\mathrm d}{\mathrm d x} (e^{\sec x})}{\frac{\mathrm d}{\mathrm d x} (e^{\sec 2x})}$
I think what you write is true as long as $L\neq0$.
Dec
15
comment Complex Function in the unit disc
@Tim: The unit disc contains $2/3$ and not $4/3$. Thus it doesn't take the unit disc to itself. However, the point is superfluous as it is the derivative and not the function itself.
Dec
15
reviewed Approve Complex Function in the unit disc
Dec
15
comment Complex Function in the unit disc
@MielSharf: I think it is $f'(2/3)=4/3$.
Dec
14
reviewed Close Greatest common divisor is divisible by every common divisor