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AryanSonwatikar
  • Member for 4 years
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  • India
24 votes
3 answers
3k views

Is it simply a coincidence that if you differentiate the formula for the volume of sphere you get the formula for the surface area of sphere? [duplicate]

15 votes
8 answers
416 views

Show that $f(x)=\sqrt 2$ has no solutions $f(x)=\sin x\cos x(2+\sin x)$ and $x\in [0,\frac{\pi}{2}]$.

5 votes
1 answer
107 views

Rational points of an circle centred at $(\pi,2)$

4 votes
4 answers
127 views

If distinct integers $a,b,c,d$ are consecutive terms of an arithmetic progression such that . . .

4 votes
2 answers
307 views

Let $p=1+\frac{1}{\sqrt 2}+\cdots\frac{1}{\sqrt {120}}$ and $q=\frac{1}{\sqrt 2}+\frac{1}{\sqrt 3}+\cdots\frac{1}{\sqrt {121}}$ then

4 votes
3 answers
138 views

Computing $\int_0^1 \frac{\arcsin \sqrt x}{x^2-x+1} dx$ [duplicate]

4 votes
2 answers
99 views

Decoding $\int_{\frac 12}^{2} \frac{\ln t}{1+t^n}dt$

3 votes
2 answers
118 views

Simpler ways of finding solutions to $\int_0^x \lfloor{x\rfloor}^2 dx=2(x-1)$

3 votes
2 answers
101 views

Probability that $|z_1+z_2|\geq \sqrt{2+\sqrt 3}$

3 votes
3 answers
156 views

Evaluate: $\int\limits_{e}^{e^4} \sqrt{\ln x} dx$

3 votes
1 answer
231 views

Why is the surface area of a sphere equal to $4\pi r^2$ [duplicate]

3 votes
1 answer
87 views

Solving $\int \frac{dx}{x\ln x}$ [duplicate]

2 votes
1 answer
194 views

If $z_1,\dotsc,z_n$ are the vertices of a regular $n$-gon, with $z_3 + z_n = Az_1 + \bar{A}z_2$, find $\lfloor |A| \rfloor$.

2 votes
2 answers
185 views

Proving that almost all numbers are good.

2 votes
3 answers
1k views

Sum of certain consecutive numbers is $1000$.

2 votes
4 answers
55 views

$f(2-x)=f(2+x)$ and $f'(1/2)=0=f'(1)$. Find minimum number of roots of $f''(x)=0$.

2 votes
2 answers
84 views

$\frac{dy}{dx}=\frac{y^3}{e^x +y^2}$

2 votes
1 answer
76 views

Ascending order of $3^a-3^b+3^c-3^d+3^e$.

2 votes
1 answer
93 views

A cake problem reduced to recursion.

2 votes
2 answers
82 views

$\lim_\limits{x\to 0^{+}} \frac{\arcsin(1-\{x\})\arccos(1-\{x\})}{\sqrt{2\{x\}}(1-\{x\})}$

2 votes
1 answer
1k views

$\lim_\limits{x\to 0}\frac{ax^2+\sin bx+\sin cx +\sin dx}{3x^2+5x^4+7x^6}=8$

2 votes
1 answer
83 views

A functional equation involving the floor function.

2 votes
3 answers
115 views

Given $U_n=\int_0^\frac{\pi}{2} x\sin^n x dx$, find $\frac{100U_{10}-1}{U_8}$

1 vote
2 answers
93 views

Integrating a non-function - Work Done using P-V graph

1 vote
2 answers
86 views

Interesting limit involving hordes of logarithms.

1 vote
1 answer
38 views

Solving $f(x)$ having a limit with $|x^2-2|$.

1 vote
3 answers
160 views

Finding $\lim_{n\to\infty} \left(\frac{\sqrt{n^2+n}-1}{n}\right)^{2\sqrt{n^2+n}-1}$

1 vote
2 answers
60 views

Finding $\lim_{x\to a} \frac{1}{(a^2-x^2)^2}(\frac{a^2+x^2}{ax}-2\sin( \frac{a\pi}{2})\sin(\frac{x\pi}{2}))$

1 vote
1 answer
48 views

A solution to the functional equation $ f(xy) = f(x) + f(y) + \frac{x+y-1}{xy} $

1 vote
1 answer
232 views

Locus of the circumcenter of triangle formed by the axes and tangent to a given circle.