imperialist
Name:
Michael
School:
Duke University
About:
I'm currently a junior at Duke University studying math, physics, and German. I've been competing in various math competitions and olympiads for many years and greatly enjoy helping other people learn. I've taken Multivariable Calculus, Linear Algebra, Non-Euclidean Geometry, Number Theory, Differential Equations, Probability, Real Analysis, the Putnam class (3 times), 2 semesters of Complex Analysis, 2 semesters of Abstract Algebra, Topology, 2 semesters of Differential Geometry, and Representation Theory, and I'm glad to share any of that knowledge with anyone who needs help :)
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Questions Answered 114
Medals Received 123
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Medals Received 123
Questions Answered
imperialist:
This is my favorite inequality, just because it has such a beautiful proof. Show that, given four positive numbers a, b, c, d such that a+b+…
updated 2 years ago
7 replies
4 Medals
Mathematics
imperialist:
Here's a fun integral question I made for a competition a few years ago. I was inspired by this much easier question:
Warmup: Let f(x) be …
updated 2 years ago
12 replies
5 Medals
Mathematics
Nisha318:
Solve separable differential equation: <see attached>
updated 2 years ago
3 replies
1 Medal
Mathematics
chasityburton:
find the cross product of the vectors (2, -1, 4) and (6, -2,1). is the resulting vector perpendicular to the given vector?…
updated 2 years ago
1 reply
2 Medals
Mathematics
SalvatoreTRM:
Need help with this integration by parts question. The answer I gave, which is in the gray box, is wrong.
updated 2 years ago
7 replies
1 Medal
Mathematics
rld613:
Can someonehelp me prove the left cancellation property with matrices?
updated 2 years ago
92 replies
4 Medals
Mathematics
pokemon23:
Anyone know how to solve compound circuits ? involving with the math
updated 2 years ago
39 replies
2 Medals
Mathematics
watchmath:
Compute
\[\lim_{x\to +\infty} x\left(\sqrt{x^2+1}-\sqrt[3]{x^3+1}\right)\]
updated 2 years ago
56 replies
7 Medals
Mathematics
watchmath:
Given that \(a+b+c=0\). Find
\[\left(\frac{b-c}{a}+\frac{c-a}{b}+\frac{a-b}{c}\right)\left(\frac{a}{b-c}+\frac{b}{c-a}+\frac{c}{a-b}\right)\…
updated 2 years ago
8 replies
1 Medal
Mathematics
watchmath:
Let \(\{F_n\}\) be the Fibonacci sequence: \(F_0=1, F_1=1\) and \(F_n=F_n+F_{n-1}\) for \(n\geq 2\). Show that
\[\sum_{i=0}^n (n-i)F_i=F_{n+…
updated 2 years ago
9 replies
2 Medals
Mathematics
RONNCC:
I feel like asking a question:
how do you prove the integral of e^(-pi * x^2) from -infinity to infinity = 1?
updated 2 years ago
4 replies
1 Medal
Mathematics
LouC:
How to parameterize a folium curve (x^3 + y^3 - 9xy = 0)?
updated 2 years ago
2 replies
2 Medals
Mathematics
josecastaneda:
can anyone help me with integration
updated 2 years ago
20 replies
1 Medal
Mathematics
rld613:
Can someone help me prove a property of matrices?
updated 2 years ago
21 replies
3 Medals
Mathematics
UnkleRhaukus:
\[{dy \over dx}={4y^2 \over x^2}+5{y \over x}+1\]
updated 2 years ago
36 replies
6 Medals
Mathematics
mmy92:
find the integral of :
(x^4)*cos(x^3) dx
updated 2 years ago
1 reply
1 Medal
Mathematics
Broken_Fixer:
A cube with volume of 1 cm^3 has a total Edge Length of 12 (because 12 edges of length 1). Which polyhedra with volume 1 have less total Edg…
updated 2 years ago
3 replies
3 Medals
Mathematics
rld613:
Matrix question
updated 2 years ago
24 replies
2 Medals
Mathematics
mattfeury:
Can someone explain the theory behind the Fourier Transform?
updated 2 years ago
28 replies
4 Medals
Mathematics
rld613:
Can someone please explain me how to inverse a matrix?
updated 2 years ago
16 replies
1 Medal
Mathematics
britt320042000:
. Determine whether the following function is even, odd, or neither. f(x)=-7x/x^2-3
updated 2 years ago
1 reply
No Medals Yet
Mathematics
StArAnGeL:
Let * be a binary operation on the set {0, 1, 2, 3, 4, 5}, defined as a *b={(a+b, if a+b <6 & a+b-6,if a+b≥6) Show that zero is the ident…
updated 2 years ago
21 replies
3 Medals
Mathematics
stephaniiee:
(1/27) ^ 3x+2 (simplify)
updated 2 years ago
10 replies
5 Medals
Mathematics
sadafmaqbool:
what is the value of y, if 3y, 4y,and 5y are the exterior angles of a triangle?
updated 2 years ago
7 replies
2 Medals
Mathematics
Nancy_Lam:
attach file
updated 2 years ago
12 replies
1 Medal
Mathematics
mikejano13:
For what numbers theta is f(theta)=tan(theta) not defined? f(theta)=tan(theta) is not defined for numbers that are (even multiples, odd mult…
updated 2 years ago
12 replies
1 Medal
Mathematics
mikejano13:
Find the exact values of each of the remaining trig functions of theta.
sin(theta)=(-3/5) , 180*<theta<270*…
updated 2 years ago
6 replies
No Medals Yet
Mathematics
kwenisha:
Prove that if a and b positive numbers such that a+b=1, then show that (a+1/a)^2+(b+1/b)^2≥(25/2)
updated 2 years ago
26 replies
3 Medals
Mathematics
ahaikal10:
find all solutions of the given equation in the interval [0,2pi]
cosx=cos3x
updated 2 years ago
4 replies
2 Medals
Mathematics
aveytare:
We dene a relation R on the set Z of integers by nRm if n^2 -
updated 2 years ago
2 replies
No Medals Yet
Mathematics
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