User Unknown x

7 votes

1 answer

387 views

Find $\int_0^\infty \int_0^t e^{-t}\frac{\sin(\tau)}{\tau}d\tau dt$ using laplace transform.

asked Dec 23, 2020 at 5:21

5 votes

5 answers

498 views

Evaluate $\lim _{n\to \infty }\int _{0}^{1}nx^ne^{x^2}dx$

asked Aug 12, 2020 at 6:34

4 votes

0 answers

105 views

Solve $\frac{dy}{dx}=\frac{y^2}{\left(x^2+y^2\right)^{\frac{5}{2}}}.$

asked Jan 4, 2021 at 1:46

4 votes

5 answers

371 views

Suppose $|A|=n, f:A\to A$ is injective $\implies \exists k\in [n]:f^k(x)=x$

asked Dec 16, 2020 at 0:16

4 votes

1 answer

68 views

Let $F:L^3[0,2]\to \mathbb R$ defined as $F\left(f\right)=\int _0^2t^{-\frac{2}{5}}f\left(t\right)dt.$ Find $||F||$.

asked Jan 12, 2023 at 0:32

3 votes

1 answer

107 views

how many ways can the committee be formed if one women $W_1$ refuses to be in the committee if another particular women $W_2$ be included?

asked Oct 2, 2021 at 2:26

3 votes

1 answer

699 views

An operator is compact iff it maps any weakly convergent sequence to a convergent one.

asked Dec 21, 2022 at 2:01

3 votes

0 answers

55 views

Prove that the set of diagonalizable matrices is dense in $\mathbb C^{n,n}$ with respect to spectral norm. Is it true for any matrix norm? [duplicate]

asked May 16 at 9:35

2 votes

1 answer

47 views

Prove that that the function $f:\mathbb R^3\to \mathbb R$ defined by $f(x,y,z)=ye^x+xz^2$ is differentiable at the point (0,-4,2) using definition.

asked Mar 27 at 17:47

2 votes

2 answers

98 views

Prove that $\langle x, y \rangle = \overline{\langle y, x \rangle}$

asked Mar 31 at 9:40

2 votes

0 answers

60 views

Solve the differential equation $2xyy′ + 1 + y^2 = 0. $ and also find the maximal interval of the solution.

asked Nov 27, 2023 at 11:12

2 votes

1 answer

76 views

Find the solution of $2y(x−1)y′ +y^2 = 4x(3x−2)$ with initial condition $y(1)=2$ and hence find the maximal interval interval of the solution.

asked Nov 27, 2023 at 21:31

2 votes

1 answer

32 views

Substantiate the following statement " Arnoldi iteration is nothing but orthogonal projection onto Krylov subspaces"

asked Jun 5 at 9:39

2 votes

1 answer

91 views

If $A$ is symmetric positive definite, then solving $Ax = b$ is equivalent to minimizing the quadratic form $\varphi(x) = \frac{1}{2}x^T A x - x^T b$

asked Jun 9 at 9:35

2 votes

1 answer

77 views

Prove that spectrum of $A$ and $B$ are same.

asked Jan 6, 2023 at 0:20

2 votes

0 answers

118 views

How can I say that these definitions of the general integral are equivalent?

asked Jul 29, 2022 at 0:30

2 votes

1 answer

327 views

Prove that $y=-\tan^{-1}(x)$ is a decreasing function with out the help of calculus.

asked Oct 26, 2022 at 0:52

2 votes

2 answers

48 views

If an event $A$ is independent of the event $B, B\cap C \text{ and } B \cup C.$ Then find $P(A \cap C)$

asked Sep 26, 2021 at 10:28

2 votes

2 answers

92 views

A compact operator cannot be unbounded. Justify your answer.

asked Dec 16, 2022 at 6:15

2 votes

0 answers

152 views

Find the rate of convergence of the following sequences.

asked Dec 28, 2021 at 1:59

2 votes

1 answer

318 views

Any measurable function $f:X \to \mathbb R, \Sigma=\{X,\emptyset\}$(where $X$ is a non empty set) must be constant.

asked Jan 10, 2021 at 12:28

1 vote

0 answers

31 views

Show that $G:[c,d]\to \mathbb R$ defined by $G(x)=\int_0^{f(x)}F(t)dt, x\in [c,d] $ is differentiable and $G'(x)=F\circ f(x) \cdot f'(x).$

asked Dec 3, 2020 at 3:07

1 vote

1 answer

337 views

If $p_n\to p$ and $\lim _{n\to \infty }\frac{|p_{n+1}-p|}{|p_n-p|^\alpha}=0$, what can be said of the order of convergence?

asked Sep 7, 2021 at 5:42

1 vote

0 answers

49 views

Where did the author uses, injectivity and continuous differentiability of $f$?

asked Jan 6, 2021 at 16:01

1 vote

2 answers

61 views

Evaluate $\int_0^1f(t)dt$

asked Aug 12, 2020 at 10:06

1 vote

0 answers

186 views

How does $F_p$ genrated?

asked Aug 17, 2020 at 1:49

1 vote

2 answers

2k views

How does $dV=2\pi R^2t \sin \theta\, d\theta$ come?

asked Aug 19, 2020 at 11:37

1 vote

2 answers

845 views

Find the equation of the two tangent planes to the sphere $x^2+y^2+z^2-2y-6z+5=0$ which are parallel to the plane $2x+2y-z=0$

asked Jun 15, 2020 at 0:10

1 vote

2 answers

69 views

Evaluate $1-\frac{1}{3\cdot 3}+\frac{1}{5\cdot 3^2}-\frac{1}{7\cdot 3^3}+\cdots$

asked Jun 15, 2020 at 2:21

1 vote

1 answer

82 views

Let $f(x)=x^5+a_1x^4+a_2x^3+a_3x^2$ be a polynomial function. If $f(1)<0$ and $f(-1)>0$. Then

asked Jul 11, 2020 at 2:44

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116 Questions

Find $\int_0^\infty \int_0^t e^{-t}\frac{\sin(\tau)}{\tau}d\tau dt$ using laplace transform.

Evaluate $\lim _{n\to \infty }\int _{0}^{1}nx^ne^{x^2}dx$

Solve $\frac{dy}{dx}=\frac{y^2}{\left(x^2+y^2\right)^{\frac{5}{2}}}.$

Suppose $|A|=n, f:A\to A$ is injective $\implies \exists k\in [n]:f^k(x)=x$

Let $F:L^3[0,2]\to \mathbb R$ defined as $F\left(f\right)=\int _0^2t^{-\frac{2}{5}}f\left(t\right)dt.$ Find $||F||$.

how many ways can the committee be formed if one women $W_1$ refuses to be in the committee if another particular women $W_2$ be included?

An operator is compact iff it maps any weakly convergent sequence to a convergent one.

Prove that the set of diagonalizable matrices is dense in $\mathbb C^{n,n}$ with respect to spectral norm. Is it true for any matrix norm? [duplicate]

Prove that that the function $f:\mathbb R^3\to \mathbb R$ defined by $f(x,y,z)=ye^x+xz^2$ is differentiable at the point (0,-4,2) using definition.

Prove that $\langle x, y \rangle = \overline{\langle y, x \rangle}$

Solve the differential equation $2xyy′ + 1 + y^2 = 0. $ and also find the maximal interval of the solution.

Find the solution of $2y(x−1)y′ +y^2 = 4x(3x−2)$ with initial condition $y(1)=2$ and hence find the maximal interval interval of the solution.

Substantiate the following statement " Arnoldi iteration is nothing but orthogonal projection onto Krylov subspaces"

If $A$ is symmetric positive definite, then solving $Ax = b$ is equivalent to minimizing the quadratic form $\varphi(x) = \frac{1}{2}x^T A x - x^T b$

Prove that spectrum of $A$ and $B$ are same.

How can I say that these definitions of the general integral are equivalent?

Prove that $y=-\tan^{-1}(x)$ is a decreasing function with out the help of calculus.

If an event $A$ is independent of the event $B, B\cap C \text{ and } B \cup C.$ Then find $P(A \cap C)$

A compact operator cannot be unbounded. Justify your answer.

Find the rate of convergence of the following sequences.

Any measurable function $f:X \to \mathbb R, \Sigma=\{X,\emptyset\}$(where $X$ is a non empty set) must be constant.

Show that $G:[c,d]\to \mathbb R$ defined by $G(x)=\int_0^{f(x)}F(t)dt, x\in [c,d] $ is differentiable and $G'(x)=F\circ f(x) \cdot f'(x).$

If $p_n\to p$ and $\lim _{n\to \infty }\frac{|p_{n+1}-p|}{|p_n-p|^\alpha}=0$, what can be said of the order of convergence?

Where did the author uses, injectivity and continuous differentiability of $f$?

Evaluate $\int_0^1f(t)dt$

How does $F_p$ genrated?

How does $dV=2\pi R^2t \sin \theta\, d\theta$ come?

Find the equation of the two tangent planes to the sphere $x^2+y^2+z^2-2y-6z+5=0$ which are parallel to the plane $2x+2y-z=0$

Evaluate $1-\frac{1}{3\cdot 3}+\frac{1}{5\cdot 3^2}-\frac{1}{7\cdot 3^3}+\cdots$

Let $f(x)=x^5+a_1x^4+a_2x^3+a_3x^2$ be a polynomial function. If $f(1)<0$ and $f(-1)>0$. Then