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Adhvaitha's user avatar
Adhvaitha's user avatar
Adhvaitha's user avatar
Adhvaitha
  • Member for 9 years, 2 months
  • Last seen more than 3 years ago
153 votes
Accepted

Identification of a quadrilateral as a trapezoid, rectangle, or square

37 votes
Accepted

Write 100 as the sum of two positive integers

32 votes

Calculate in closed form $\int_0^1 \int_0^1 \frac{dx\,dy}{1-xy(1-x)(1-y)}$

22 votes

$\lim_{n\rightarrow \infty}(3^n+7^n)^{1/n}$

19 votes
Accepted

If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.

19 votes
Accepted

Showing that ln$(xy)$ = ln $x$+ln $y$

17 votes
Accepted

Find $\lim_{n\to \infty} \int_n^{n+1} {\sin x \over x} dx$

16 votes

Can this be shown: $\sqrt[3]{a\sqrt[3]{a\sqrt[3]{a\dots}}} = \sqrt a$?

15 votes

What are some math concepts which were originally inspired by physics?

14 votes
Accepted

Given $\frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}$ show that $x^{b+c-a}\cdot y^{c+a-b}\cdot z^{a+b-c} = 1$

13 votes

Prove QM-AM inequality

12 votes

Is there an opposite to the Squeeze theorem?

12 votes
Accepted

Proving $\pi=2\sum_{n=0}^{\infty} \arctan \frac{1}{F_{2n+1}}$

11 votes
Accepted

How to evaluate this definite integral: $\int_3^6 \frac{\sqrt x}{\sqrt x+\sqrt{9-x}} dx$

11 votes
Accepted

Intriguing Indefinite Integral: $\int ( \frac{x^2-3x+1/3 }{x^3-x+1})^2 \mathrm{d}x$

10 votes
Accepted

Compute $\int_{0}^{\infty}\frac{x \log(x)}{(1+x^2)^2}dx$

10 votes
Accepted

Dominated Convergence Theorem

10 votes

Prove that $f=x^4-4x^2+16\in\mathbb{Q}[x]$ is irreducible

10 votes

Determining limit of recursive sequence

10 votes
Accepted

Proving $\sqrt{2a + 2\sqrt{a^2 - b}}=\sqrt{a-\sqrt{b}} + \sqrt{a+\sqrt{b}}$, where $a\geq 0,\ b\geq 0$.

10 votes
Accepted

Prove that all the roots of $p(x)=F_{n}x^{n}+..+F_{1}x+F_{0}$ can't be real

10 votes

Evaluate $\lim_{x\to\infty}\left(1+\frac 4x\right)^{\frac x8}$

9 votes

Taylor series $\ln(1+e^x)$ about $x=0$

9 votes
Accepted

Show that the sequence $x_{n+1}=x_n(2-x_n)$ is convergent

9 votes

The minimum value of $ f(x) = | x - 1 | + | x - 2 | + | x - 3 | $ is?

9 votes
Accepted

Prove that $\frac{1+ab}{1+a}+\frac{1+bc}{1+b}+\frac{1+ac}{1+c} \geq 3.$

9 votes

Find the limit of $\lim_{n\to \infty} (1+n)^{\frac1n}$

9 votes

Problem : $\int^{\pi/2}_0 \sin\theta \ln(\sin\theta)d\theta$ is equal to ....

9 votes
Accepted

Taylor expansion $\ln(1+x+x^2)$ about $x=0$

9 votes

If three complex numbers $z_k$ have modulus $1$, then $|z_1+z_2+z_3| = \left|\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3}\right|$

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