User Darshan P.

6 votes

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Derivative of ${g(x)=\int_0^1 \frac{e^{-x^2(t^2+1)}}{t^2+1}\,dt}$ respect to $x$.

answered Nov 13, 2021 at 11:13

5 votes

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Which of the two quantities $\sin 28^{\circ}$ and $\tan 21^{\circ}$ is bigger .

answered Jan 20, 2022 at 13:19

4 votes

Sum of Squares of Harmonic Numbers

answered Nov 15, 2021 at 14:30

3 votes

Representing the cyclic differentiation pattern of $\frac{d^n}{dx^n}(\sin(x))$ using linear algebra.

answered Nov 22, 2021 at 16:05

3 votes

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How do I find $\;\lim_{n\to\infty}n\int_{0}^{1} \frac{x^n}{x^2+1} dx\;$?

answered Jan 25, 2022 at 17:55

2 votes

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How does this algorithm that multiplies $(1 + x)(1 + x^2)(1 + x^3)(1 + x^4)...$ work?

answered Jan 23, 2022 at 10:28

2 votes

Using cross product find direction vector of line joining point of intersection of line and plane and foot of perpendicular from line to plane.

answered Nov 23, 2021 at 8:10

2 votes

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If $f(s) =\frac{s}{\sqrt{1-s^2}}$, how to evaluate $\lim_{s\to \pm\infty}f^{-1}(s)$?

answered Jan 16, 2022 at 10:49

2 votes

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Curvature as a rate of change in slope

answered Jan 16, 2022 at 7:00

2 votes

A problem when trying to compute the derivative of $\frac {e^{-x}x}{x+2}$

answered Jan 16, 2022 at 7:31

2 votes

How does being monotonic increasing and bounded above imply that the sequence $a_n=\left ( 1+\frac{1}{n}\right)^n$ converges to $e$?

answered Nov 19, 2021 at 16:47

2 votes

Proof without words that $\tan ^{-1} 2-\tan ^{-1}\left(\frac{3}{2}\right)=\cot ^{-1} 8$

answered Nov 15, 2021 at 16:47

2 votes

Accepted

Circle formula that touches $X$ and $Y$ axes and passes $(2, -1)$

answered Nov 18, 2021 at 11:28

2 votes

How to find following limit of sequence?

answered Nov 14, 2021 at 14:52

2 votes

Accepted

The harmonic Series sequence.

answered Nov 14, 2021 at 10:35

2 votes

Show that $\frac{1+z}{1-z}$ = $i\cot(\frac{\theta}{2})$

answered Feb 16, 2022 at 7:41

2 votes

Improper integrals with bounds 0 to infinity

answered Dec 1, 2022 at 7:45

2 votes

Accepted

General solution to $\int \frac{1}{x^n +1}dx$ where $n$ is an integer?

answered Dec 2, 2022 at 6:01

2 votes

2015 Cambridge Entrance Examination Q6

answered Jan 18, 2022 at 8:09

2 votes

Combinatorially proving $\sum_{k=0}^{n} \binom{4n}{4k} = 2^{4n-2} + (-1)^{n}2^{2n-1}$

answered Jul 20, 2023 at 19:11

1 vote

$\log_{3}\frac{16^{x-3}+14}{4^{x-3}+2}=243$ , find the value of $x$.

answered Jul 5, 2022 at 10:29

1 vote

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$\sum_{i=1}^{n} \frac {x^{2i-1}}{\sqrt{2i}}$ as polylogarithm

answered Nov 30, 2022 at 12:45

1 vote

Why doesn't fixed point iteration for $2x^3-4x^2+x+1$ work for the initial value of 2?

answered Jan 31, 2022 at 14:38

1 vote

Accepted

If $f(x)=x^3+e^\frac{x}{2}$, compute $\frac{d}{dx} \left(f^{-1}(x)\right) \text{at$~~x=1$}$

answered Nov 13, 2021 at 8:38

1 vote

Prove that $1+e^{\frac{-1}{x}}+2x(e^{\frac{-1}{x}}-1) >0 $ when $x >0$

answered Nov 15, 2021 at 15:18

1 vote

Why the square root of any decimal number between 0 and 1 always come out to be greater than the number itself?

answered Nov 15, 2021 at 8:38

1 vote

Proving $\sec^{-1}(z) = -i\log\left[ \frac{1}{z} + \left(\frac{1}{z^2} - 1 \right)^{1/2}\right]$

answered Nov 22, 2021 at 3:42

1 vote

Finding similar series

answered Nov 22, 2021 at 13:30

1 vote

Accepted

How do you determine that the characteristic polynomial is the minimal polynomial?

answered Dec 7, 2021 at 8:04

1 vote

Prove $5^n > n^5 $ for $n≥6$

answered Dec 8, 2021 at 7:54

Stack Exchange Network

47 Answers

Derivative of ${g(x)=\int_0^1 \frac{e^{-x^2(t^2+1)}}{t^2+1}\,dt}$ respect to $x$.

Which of the two quantities $\sin 28^{\circ}$ and $\tan 21^{\circ}$ is bigger .

Sum of Squares of Harmonic Numbers

Representing the cyclic differentiation pattern of $\frac{d^n}{dx^n}(\sin(x))$ using linear algebra.

How do I find $\;\lim_{n\to\infty}n\int_{0}^{1} \frac{x^n}{x^2+1} dx\;$?

How does this algorithm that multiplies $(1 + x)(1 + x^2)(1 + x^3)(1 + x^4)...$ work?

Using cross product find direction vector of line joining point of intersection of line and plane and foot of perpendicular from line to plane.

If $f(s) =\frac{s}{\sqrt{1-s^2}}$, how to evaluate $\lim_{s\to \pm\infty}f^{-1}(s)$?

Curvature as a rate of change in slope

A problem when trying to compute the derivative of $\frac {e^{-x}x}{x+2}$

How does being monotonic increasing and bounded above imply that the sequence $a_n=\left ( 1+\frac{1}{n}\right)^n$ converges to $e$?

Proof without words that $\tan ^{-1} 2-\tan ^{-1}\left(\frac{3}{2}\right)=\cot ^{-1} 8$

Circle formula that touches $X$ and $Y$ axes and passes $(2, -1)$

How to find following limit of sequence?

The harmonic Series sequence.

Show that $\frac{1+z}{1-z}$ = $i\cot(\frac{\theta}{2})$

Improper integrals with bounds 0 to infinity

General solution to $\int \frac{1}{x^n +1}dx$ where $n$ is an integer?

2015 Cambridge Entrance Examination Q6

Combinatorially proving $\sum_{k=0}^{n} \binom{4n}{4k} = 2^{4n-2} + (-1)^{n}2^{2n-1}$

$\log_{3}\frac{16^{x-3}+14}{4^{x-3}+2}=243$ , find the value of $x$.

$\sum_{i=1}^{n} \frac {x^{2i-1}}{\sqrt{2i}}$ as polylogarithm

Why doesn't fixed point iteration for $2x^3-4x^2+x+1$ work for the initial value of 2?

If $f(x)=x^3+e^\frac{x}{2}$, compute $\frac{d}{dx} \left(f^{-1}(x)\right) \text{at$~~x=1$}$

Prove that $1+e^{\frac{-1}{x}}+2x(e^{\frac{-1}{x}}-1) >0 $ when $x >0$

Why the square root of any decimal number between 0 and 1 always come out to be greater than the number itself?

Proving $\sec^{-1}(z) = -i\log\left[ \frac{1}{z} + \left(\frac{1}{z^2} - 1 \right)^{1/2}\right]$

Finding similar series

How do you determine that the characteristic polynomial is the minimal polynomial?

Prove $5^n > n^5 $ for $n≥6$