Shivansh Jaiswal's user avatar
Shivansh Jaiswal's user avatar
Shivansh Jaiswal's user avatar
Shivansh Jaiswal
  • Member for 2 years, 6 months
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3 votes
1 answer
203 views

Confusion about limits of integration

3 votes
1 answer
70 views

Proving that product of roots does not exceed $\frac{1}{2^n}$ if $|f(0)| = f(1)$ and the roots lie between 0 to 1.

3 votes
2 answers
149 views

Minimizing perimeter and area of the section obtained by intersection of a given line passing through a point, and the conic.

3 votes
3 answers
137 views

Evaluate $ \int \frac{x^4 + 1}{(x^4 - 1)^2}dx $

2 votes
3 answers
128 views

Evaluating the limit $ L = \lim_{n \rightarrow \infty} \left(1+\frac{1\cdot n + 2 \cdot (n-1) + ... + n \cdot 1}{1^3 + 2^3 + ... + n^3} \right)^{n} $

2 votes
0 answers
134 views

Proving $x + \sin x + \sin(x + \sin x) + \sin(x + \sin x + \sin(x + \sin x)) + ... = \pi $ [duplicate]

2 votes
1 answer
59 views

Computing $\sum_{n=1}^{\infty} \frac{e^{-An}sin(Bn)}{n}$, where $A,B$ are constants.

1 vote
3 answers
107 views

For polynomial $x^3 + x^2 - 4x + 1$, values of $\frac{\alpha}{\beta} + \frac{\beta}{\gamma} + \frac{\gamma}{\alpha}$

1 vote
1 answer
166 views

How to find values of the given $4n^2 - 5n + 16$ for which the function is a perfect square?

1 vote
0 answers
77 views

Need help in evaluating the integral $\frac{dx}{(x^4 - 1)^2}$ [duplicate]

1 vote
2 answers
73 views

Minimizing $2a^2 + b^2 + c^2$ given $4a + 3b + c = 7$

1 vote
1 answer
118 views

Evaluating an integral involving $xe^{-x^2 / 2}$ and a similar infinite series.

0 votes
0 answers
54 views

Analytic continuation of the $\arccos{x}$ function.

0 votes
1 answer
70 views

Minima of $\frac{a+b+c}{b-a}$ for a,b,c in $f(x) = ax^2 + bx + c \geq 0$ and $a < b$

0 votes
1 answer
50 views

$\sum_{cyc} \alpha(\alpha + a)(\alpha^2 +a+b) = 4$ where $\alpha, \beta, \gamma, \delta$ are the roots of $x^4 + ax^3 + (a+b)x^2 + a(a + b)x - 1$

0 votes
2 answers
186 views

Find the number of positive real values of $a$, such that $a^2 x^2 + ax - 1 + 7a^2$ has $2$ distinct integer roots