User Ahaan S. Rungta

20 votes

Why rationalize the denominator?

answered Dec 29, 2014 at 19:32

17 votes

Accepted

Show that $\sqrt{2+\sqrt{2+\sqrt{2...}}}$ converges to 2

real-analysis sequences-and-series nested-radicals

answered Nov 7, 2013 at 16:29

16 votes

Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?

calculus sequences-and-series harmonic-numbers

answered Nov 1, 2013 at 17:38

13 votes

Evaluating $\int\frac{\sqrt{x^2-1}}x\mathrm dx$

calculus integration indefinite-integrals

answered Jan 14, 2015 at 20:46

12 votes

Accepted

Did I take the derivative correctly? $x^y=y^x$

real-analysis derivatives solution-verification

answered Nov 1, 2013 at 20:58

12 votes

Accepted

Find zeros of function $f(x)$

calculus algebra-precalculus

answered Dec 1, 2013 at 15:49

10 votes

Accepted

Integral of $x(1-x^2)^n$

integration

answered Jan 1, 2015 at 2:49

10 votes

Is it possible to define $\lceil x\rceil$ in terms of $\lfloor\ldots\rfloor$?

algebra-precalculus definition ceiling-and-floor-functions

answered Dec 28, 2014 at 21:27

10 votes

Accepted

How to simplify expression with exponents?

arithmetic

answered Dec 27, 2014 at 22:31

10 votes

How to evaluate $ \int \sec^3x \, \mathrm{d}x$?

integration

answered Dec 23, 2014 at 16:04

9 votes

Why is $2^n$ the maximum number of subsets of a set of size $n$?

discrete-mathematics

answered Nov 12, 2013 at 15:01

9 votes

Do non-square matrices have eigenvalues?

eigenvalues-eigenvectors

answered Nov 27, 2013 at 23:22

7 votes

Accepted

Parametric Equations: Find $\frac{\mathrm d^2y}{\mathrm dx^2}$.

calculus derivatives parametric

answered Nov 21, 2013 at 17:18

7 votes

Accepted

Given $f(x)$ and $g(x)$, find $(fg)(x)$

algebra-precalculus functions solution-verification

answered Dec 17, 2014 at 15:06

6 votes

The sum of the $n$ smallest odd numbers is equal to $n^2$

algebra-precalculus

answered Aug 26, 2014 at 23:41

6 votes

Accepted

What is difference between ≈ and ~?

notation

answered Aug 29, 2014 at 0:00

5 votes

Accepted

How to evaluate $\lim\limits_{n\rightarrow \infty} \sin (1/n)$?

limits trigonometry proof-verification

answered Dec 11, 2014 at 18:10

5 votes

Beautiful, simple proofs worthy of writing on this beautiful glass door

soft-question proof-writing recreational-mathematics

answered Aug 27, 2014 at 20:37

5 votes

Accepted

Squarefree binomial coefficients.

number-theory binomial-coefficients

answered Nov 28, 2013 at 16:57

5 votes

What is $\frac{d(\arctan(x))}{dx}$?

calculus trigonometry derivatives

answered Nov 28, 2013 at 15:30

5 votes

Accepted

2014 Fall OMO #28

algebra-precalculus contest-math

answered Dec 19, 2014 at 12:47

5 votes

Accepted

Evaluate $ \lim\limits_{x\to 1} \frac{(\ln x)^2}{1-x} $

sequences-and-series limits

answered Dec 21, 2014 at 15:01

5 votes

Accepted

Finding $ \int_0^1 \frac {\ln x}{1+x^2}\mathrm dx $

calculus integration definite-integrals improper-integrals closed-form

answered Dec 20, 2014 at 18:32

4 votes

Equality of mixed partial derivatives

multivariable-calculus partial-derivative

answered Dec 20, 2014 at 16:59

4 votes

Accepted

Continued fraction to irrational number

elementary-number-theory continued-fractions

answered Dec 28, 2014 at 21:09

4 votes

Accepted

$ \int_{ABC} f = \int_{CDA} f $

calculus integration

answered Dec 17, 2014 at 14:06

4 votes

Solve $\sin2x +\sin x = 0$ algebraically

algebra-precalculus trigonometry

answered Dec 17, 2014 at 14:13

4 votes

FoxTrot Bill Amend Problems

calculus integration algebra-precalculus limits derivatives

answered Nov 22, 2013 at 16:20

4 votes

Accepted

Prove by mathematical induction: $n < 2^n$

inequality induction

answered Oct 21, 2013 at 15:57

4 votes

Why do we write complex numbers as $e^{i \theta} $?

complex-numbers

answered Oct 22, 2013 at 14:25

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191 Answers

Why rationalize the denominator?

Show that $\sqrt{2+\sqrt{2+\sqrt{2...}}}$ converges to 2

Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?

Evaluating $\int\frac{\sqrt{x^2-1}}x\mathrm dx$

Did I take the derivative correctly? $x^y=y^x$

Find zeros of function $f(x)$

Integral of $x(1-x^2)^n$

Is it possible to define $\lceil x\rceil$ in terms of $\lfloor\ldots\rfloor$?

How to simplify expression with exponents?

How to evaluate $ \int \sec^3x \, \mathrm{d}x$?

Why is $2^n$ the maximum number of subsets of a set of size $n$?

Do non-square matrices have eigenvalues?

Parametric Equations: Find $\frac{\mathrm d^2y}{\mathrm dx^2}$.

Given $f(x)$ and $g(x)$, find $(fg)(x)$

The sum of the $n$ smallest odd numbers is equal to $n^2$

What is difference between ≈ and ~?

How to evaluate $\lim\limits_{n\rightarrow \infty} \sin (1/n)$?

Beautiful, simple proofs worthy of writing on this beautiful glass door

Squarefree binomial coefficients.

What is $\frac{d(\arctan(x))}{dx}$?

2014 Fall OMO #28

Evaluate $ \lim\limits_{x\to 1} \frac{(\ln x)^2}{1-x} $

Finding $ \int_0^1 \frac {\ln x}{1+x^2}\mathrm dx $

Equality of mixed partial derivatives

Continued fraction to irrational number

$ \int_{ABC} f = \int_{CDA} f $

Solve $\sin2x +\sin x = 0$ algebraically

FoxTrot Bill Amend Problems

Prove by mathematical induction: $n < 2^n$

Why do we write complex numbers as $e^{i \theta} $?