User John Joy

57 votes

How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?

answered Sep 7, 2014 at 21:44

51 votes

How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?

answered Dec 11, 2014 at 17:17

27 votes

Accepted

How do I determine if the following function is periodic?

answered Nov 3, 2014 at 14:21

19 votes

Inequality with (1-x) as denominator

answered Apr 22, 2015 at 13:45

16 votes

Accepted

How to make a "function"?

answered Jan 30, 2015 at 16:24

15 votes

Why does cross product give a vector which is perpendicular to a plane

answered Apr 18, 2014 at 15:39

14 votes

Show that: $\sinh^{-1}(x) = \ln(x + \sqrt{x^2 +1 } )$

answered Apr 26, 2015 at 8:40

11 votes

Accepted

which is larger: $\sin(4^\circ)$ or $2\sin(2^\circ)$?

answered Dec 29, 2019 at 16:02

10 votes

Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction

answered Dec 27, 2014 at 6:27

9 votes

Taylor expansion, integration by parts, and the integration of dt.

answered Apr 8, 2014 at 16:44

9 votes

how to find surface area of a sphere

answered May 2, 2014 at 21:34

9 votes

How is $x \leq x^2$ false?

answered Jul 31, 2015 at 12:36

7 votes

Find the number of bicycles and tricycles

answered Jan 15, 2016 at 16:07

6 votes

Evaluate $\int{\frac{1}{\sin x + \cos x}}dx$

answered Dec 27, 2015 at 16:12

6 votes

Is there a chain rule for integration?

answered Feb 1, 2016 at 15:32

6 votes

Find the value of $\sin(90-a)$

answered Nov 13, 2014 at 15:29

6 votes

Accepted

Is $\frac{5x}{3}$ The Same As $\frac{5}{3}x$?

answered Dec 1, 2014 at 20:50

6 votes

Algebraic proof of $\tan x>x$

answered Jul 30, 2014 at 0:34

5 votes

Prove that $\lim_{x\rightarrow 1}{\frac{x^n-1}{x-1}}=n$ for all integer n without L'Hôpital

answered Jul 14, 2014 at 1:19

5 votes

$\sec\theta$ never equals $\tan\theta$. Or does it?!?

answered Jan 20, 2015 at 14:47

5 votes

Another way proof $1/2-1/3=1/6$ by using picture?

answered Jul 28, 2018 at 6:38

4 votes

How to know that $2n^3+9n^2+13n+6$ factors into $(n+1)(n+2)(2n+3)$?

answered Sep 30, 2018 at 1:47

4 votes

$\lim_{x\to 0} \frac{1-\cos(x)}{x\cos(x)} $ without L'hopital

answered Mar 25, 2016 at 16:48

4 votes

Integration being the opposite of differentiation?

answered Aug 25, 2014 at 21:19

4 votes

Can an inflection exist if there's no max/min?

answered Jul 26, 2014 at 14:55

4 votes

Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction

answered Nov 23, 2014 at 2:31

4 votes

Accepted

a geometric interpretation of a line integral

answered Apr 22, 2014 at 14:51

4 votes

Accepted

Basic trigonometry identities question

answered Jun 27, 2014 at 14:04

3 votes

Proof that $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$

answered Jul 29, 2014 at 15:09

3 votes

Logorithms on a first level learning

answered Jun 23, 2014 at 14:49

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520 Answers

How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?

How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?

How do I determine if the following function is periodic?

Inequality with (1-x) as denominator

How to make a "function"?

Why does cross product give a vector which is perpendicular to a plane

Show that: $\sinh^{-1}(x) = \ln(x + \sqrt{x^2 +1 } )$

which is larger: $\sin(4^\circ)$ or $2\sin(2^\circ)$?

Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction

Taylor expansion, integration by parts, and the integration of dt.

how to find surface area of a sphere

How is $x \leq x^2$ false?

Find the number of bicycles and tricycles

Evaluate $\int{\frac{1}{\sin x + \cos x}}dx$

Is there a chain rule for integration?

Find the value of $\sin(90-a)$

Is $\frac{5x}{3}$ The Same As $\frac{5}{3}x$?

Algebraic proof of $\tan x>x$

Prove that $\lim_{x\rightarrow 1}{\frac{x^n-1}{x-1}}=n$ for all integer n without L'Hôpital

$\sec\theta$ never equals $\tan\theta$. Or does it?!?

Another way proof $1/2-1/3=1/6$ by using picture?

How to know that $2n^3+9n^2+13n+6$ factors into $(n+1)(n+2)(2n+3)$?

$\lim_{x\to 0} \frac{1-\cos(x)}{x\cos(x)} $ without L'hopital

Integration being the opposite of differentiation?

Can an inflection exist if there's no max/min?

Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction

a geometric interpretation of a line integral

Basic trigonometry identities question

Proof that $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$

Logorithms on a first level learning