Question

If the sum of any finite terms in a sequnce is less than or equal to epsilon, then prove that the infinite sum is also less than or equal to epsilon.

score 518 · Answer 1 · 2026-05-13 18:48:51

518

Views

If the sum of any finite terms in a sequnce is less than or equal to epsilon, then prove that the infinite sum is also less than or equal to epsilon.

Published on 13 May 2026 - 18:48

score 70 · Answer 2 · 2026-04-19 12:56:41

70

Views

Show that $\ x_n$ is correctly defined if $2^{x_n}+3^{x_n}= n$

Published on 19 Apr 2026 - 12:56

score 54 · Answer 3 · 2026-05-05 09:16:07

54

Views

Given $\alpha(x,y,z) = \alpha_1\hat x +\alpha_2 \hat y+\alpha_3 \hat z$, how to write in the coordinates $\hat r, \hat \theta, \hat \phi$

Published on 05 May 2026 - 9:16

score 133 · Answer 4 · 2026-04-16 13:10:11

The nature of the subset $\{a\cdot b : a \in A \text{ , } b \in B\}$ where $A$ and $B$ are different subsets of $\Bbb R$ and $\Bbb R^n$ respectively

score 676 · Answer 5 · 2026-05-15 04:12:45

676

Views

integral of continuous function over [0,1] is equal to some upper bound of the function implies function is constant

Published on 15 May 2026 - 4:12

score 137 · Answer 6 · 2026-05-10 21:50:22

137

Views

Find the infimum and supremum (assignment)

Published on 10 May 2026 - 21:50

score 50 · Answer 7 · 2026-05-05 09:14:15

50

Views

How to show that $\cos(x_0)\leq \cos(x)+(x-x_0)\left[\sin(x_0)+\frac{(x-x_0)}{2}\right]$?

Published on 05 May 2026 - 9:14

score 66 · Answer 8 · 2026-05-15 04:16:18

66

Views

Prove that $\lim_{n \to \infty} (\int ^b_af(x)^n dx)^\frac{1}{n}=\sup _{x \in [a,b]} f(x)$

Published on 15 May 2026 - 4:16

score 82 · Answer 9 · 2026-04-16 11:40:45

82

Views

How to show that $\lim a_n\geq\lim b_n$?

Published on 16 Apr 2026 - 11:40

score 2.4k · Answer 10 · 2026-05-10 14:03:43

2.4k

Views

Proving that the exponential function is not uniformly continuous

Published on 10 May 2026 - 14:03

score 981 · Answer 11 · 2026-04-13 00:44:58

981

Views

Once Continuously Differentiable?

Published on 13 Apr 2026 - 0:44

score 80 · Answer 12 · 2026-05-14 09:02:32

80

Views

Which infinite series is this - $\sum_{n=1}^{\infty} n^{p}x^n$

Published on 14 May 2026 - 9:02

score 59 · Answer 13 · 2026-04-16 06:18:06

59

Views

Prove that the series $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{\sqrt{n}}$ is convergent by Cauchy Criterion.

Published on 16 Apr 2026 - 6:18

score 376 · Answer 14 · 2026-04-10 07:18:22

376

Views

Optimization of a non smooth function using a smooth approximation.

Published on 10 Apr 2026 - 7:18

score 121 · Answer 15 · 2026-05-10 17:15:02

121

Views

When are you allowed to say $\int_\mathbb{R} \mathbb{1}_{(0,1)}(x)x^{\alpha p}d\lambda = \int_0^1x^{\alpha p}dx$?

Published on 10 May 2026 - 17:15

List Question

If the sum of any finite terms in a sequnce is less than or equal to epsilon, then prove that the infinite sum is also less than or equal to epsilon.

Show that $\ x_n$ is correctly defined if $2^{x_n}+3^{x_n}= n$

Given $\alpha(x,y,z) = \alpha_1\hat x +\alpha_2 \hat y+\alpha_3 \hat z$, how to write in the coordinates $\hat r, \hat \theta, \hat \phi$

The nature of the subset $\{a\cdot b : a \in A \text{ , } b \in B\}$ where $A$ and $B$ are different subsets of $\Bbb R$ and $\Bbb R^n$ respectively

integral of continuous function over [0,1] is equal to some upper bound of the function implies function is constant

Find the infimum and supremum (assignment)

How to show that $\cos(x_0)\leq \cos(x)+(x-x_0)\left[\sin(x_0)+\frac{(x-x_0)}{2}\right]$?

Prove that $\lim_{n \to \infty} (\int ^b_af(x)^n dx)^\frac{1}{n}=\sup _{x \in [a,b]} f(x)$

How to show that $\lim a_n\geq\lim b_n$?

Proving that the exponential function is not uniformly continuous

Once Continuously Differentiable?

Which infinite series is this - $\sum_{n=1}^{\infty} n^{p}x^n$

Prove that the series $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{\sqrt{n}}$ is convergent by Cauchy Criterion.

Optimization of a non smooth function using a smooth approximation.

When are you allowed to say $\int_\mathbb{R} \mathbb{1}_{(0,1)}(x)x^{\alpha p}d\lambda = \int_0^1x^{\alpha p}dx$?

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