sonu
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2 answers
5 votes
1k views
2 bookmarks
Evaluate $\int \frac{a^2\sin^2 x+b^2\cos^2 x}{a^4\sin^2 x+b^4\cos^2 x}dx$
2 answers
4 votes
349 views
3 bookmarks
Finding area of the parallelogram enclosing the ellipse.
1 answers
3 votes
202 views
2 bookmarks
Area of the region enclosed by the three circles that have sides of a triangle as diameters.
1 answers
2 votes
1k views
1 bookmarks
Find the dual space and dual basis of basis $\beta$ in vector space $\mathbb{C^3}$
2 answers
1 votes
183 views
1 bookmarks
conditional expectation $E[{X_1}^2+{X_2}^2|X_1+X_2=t] $ of normal distributed variables
1 answers
1 votes
474 views
number of subsets that has no two consecutive elements
1 answers
1 votes
280 views
2 bookmarks
Number of nine-digit strings that contain each of the odd digits
2 answers
1 votes
338 views
If $2 (\cos \alpha-\cos\beta)+\cos\alpha\cos\beta=1$, then $p\tan\frac{\alpha}{2}+q\tan\frac{\beta}{2}=0$ for which choices of $p$ and $q$?
1 answers
1 votes
66 views
If two functions are linearly dependent on an interval then prove that their wronskian is identically zero on that interval.
1 answers
1 votes
72 views
1 bookmarks
Calculate the double limit $\lim_{n\to\infty}(\lim_{k\to\infty}\int_{0}^{1}\left ( \frac{[kx]}{k} \right )^{n}dx))$
2 answers
1 votes
135 views
2 bookmarks
Prove that $\sin x+\binom n1\sin {2x}+\binom n2\sin {3x} +...+\binom nn\sin {(n+1)x}=2^n.\cos^n \frac x2.\sin (\frac {n+2}2)x$
1 answers
1 votes
34 views
Find the equation of side $AB$ given, point $A$,equation of $i)$ median through $ $B and $ii)$ angle bisector of $C$
1 answers
1 votes
102 views
1 bookmarks
Nature of the improper integral $\int_1^∞ \frac{x^2}{(1+x^2)^2\sqrt{\log x}}\text{d}x$
2 answers
1 votes
52 views
2 bookmarks
Proving derivabiliy of multivariable function. Is polar transformation helpful?
0 answers
0 votes
39 views
number of ways, n can be written as a product of k integers
1 answers
0 votes
87 views
Equivalence of input-restricted and output-restricted deques
1 answers
0 votes
269 views
for poisson distribution, show that $P(0<X<2(\lambda +1)) \ge \frac \lambda{\lambda +1}$
2 answers
0 votes
81 views
If $E(Y\mid X)=a+bX$, show that $b =\frac{\mathrm{Cov}(X,Y)}{\mathrm{Var}(X)}$ without assuming $(X,Y)$ has bivariate normal distribution?
0 answers
0 votes
63 views
for characteristic function $\phi$, prove that $1-|\phi(2u)|^2\le 4( 1-|\phi(u)|^2 )$
2 answers
0 votes
133 views
2 bookmarks
prove that there exists no integer in $\pm\frac1k \pm \frac1{k+1}\pm\frac1{k+2}...\pm\frac1{k+n} $
1 answers
0 votes
72 views
Find $p,q$ if $(2,3)$ is circumcentre of the triangle surrounded by sides $2x+y=0, x-y-3=0$ and $x+py=q$
5 answers
0 votes
710 views
1 bookmarks
For what values of $x$ is the series convergent $\sum_{n=1}^∞ \frac{(-1)^n(x+3)^n}{n \cdot 5^n}$
3 answers
-1 votes
62 views
Taylor series $\frac{z^2+z}{(z-1)^2}$ at $z=-1$