User mmmmh mmmmmh

4 votes

1 answer

87 views

Prove that $f( \limsup \limits_{x \to +\infty} x_n)$ = $ \limsup \limits_{x \to +\infty} f(x_n)$ [closed]

asked Feb 1, 2022 at 20:26

3 votes

1 answer

175 views

Find the limit of $(1+\frac{1}{n^2})(1+\frac{2}{n^2})...(1+\frac{n}{n^2})$.

asked Feb 6, 2022 at 12:44

3 votes

4 answers

120 views

How to solve $\lfloor x \rfloor + \lfloor \frac{1}{x} \rfloor = 1$?

asked Jan 4, 2022 at 14:30

2 votes

0 answers

46 views

Question about the proof that if x is a real number then there exists a postive integer n such that -n < x < n. [closed]

asked Dec 20, 2021 at 10:21

2 votes

2 answers

470 views

How can I find the sup and inf of $m/n$ such that m,n are natural numbers and $m<2n$?

asked Dec 22, 2021 at 10:34

1 vote

0 answers

58 views

I don't know if my solution to a supremum problem is correct

asked Dec 26, 2021 at 9:37

1 vote

1 answer

78 views

A strange way to prove that $\lim_{x \to \infty} \sin(\frac{x^3}{x^2+1})$ does not exist.

asked Jan 30, 2022 at 21:34

1 vote

0 answers

47 views

A nice problem about convex functions and minimums.

asked Jan 31, 2022 at 14:49

1 vote

1 answer

67 views

Proving that $u_n = (1+ \frac{x}{n})^n$ is an increasing sequence for $n \in N$ and $n \geq |x|$.

asked Jan 12, 2022 at 8:41

1 vote

1 answer

36 views

If a function is not defined on all of its preimages set, can we talk about injectivity and surjectivity?

asked Jan 19, 2022 at 13:37

1 vote

1 answer

66 views

Find the limit of $u_n = \frac{1\times3\times5\times7\times..........\times(2n-1)}{2\times4\times6\times8\times........\times(2n)}$

asked Feb 7, 2022 at 18:08

1 vote

3 answers

62 views

How to integrate $\frac{\cos2x}{ \sin x + \sin 3x}$?

asked Mar 23, 2022 at 18:02

1 vote

1 answer

126 views

I am not sure whether my friend is saying the truth or if he's lying, how can I get the correct information out of him using logic?

asked Nov 9, 2022 at 13:50

1 vote

1 answer

57 views

Find the minimum average life of a hard disk

asked Jan 22 at 21:07

1 vote

2 answers

68 views

Can I prove the order limit theorem with a counter example? [closed]

asked Dec 6, 2021 at 12:22

1 vote

0 answers

46 views

An example of a linear map such that $Ker(f) \cap Im(f) \neq {0}$ and $f: R^2 \to R^2$ [duplicate]

asked Nov 27 at 19:27

0 votes

1 answer

69 views

What is the probability that a randomly chosen fetal heartrate differs from the mean by more than 25 bpm?

asked Jan 23 at 13:20

0 votes

1 answer

85 views

does the series $\sum | \frac{(-1)^n}{\sqrt{n}} (1+ \frac{(-1)^n}{\sqrt{n}}) |$ converge?

asked Oct 21 at 15:42

0 votes

1 answer

80 views

The limit of $ \frac{(x^2+y^2)^2}{x^2 - y^2} $ at the origin

asked Nov 24, 2022 at 17:47

0 votes

1 answer

784 views

Farthest and closest point in the circle $x^2 + y^2 = 80$ to the point (1,2)

asked Nov 5, 2022 at 16:44

0 votes

3 answers

70 views

What is the cardinality of $ \{ (A,B) \in \mathbb{P}(E)^2: A \subseteq B \}$ and $ \{ (A,B) \in \mathbb{P}(E)^2: A \cup B = E \}$

asked Feb 3, 2022 at 12:07

0 votes

0 answers

52 views

A question about the famous $\sum \frac{1}{\sqrt{n}}$ [duplicate]

asked Feb 3, 2022 at 15:56

0 votes

0 answers

24 views

How to prove the two subsequences $u_{2n}$ and $u_{2n+1}$ of the alternating harmonic series are adjacent?

asked Feb 7, 2022 at 19:41

0 votes

0 answers

16 views

Prove that if $ 0 \leq u_{n+1} \leq \frac{u_n + \epsilon_n}{K}$ then $\lim u_n = 0$.

asked Feb 13, 2022 at 17:53

0 votes

1 answer

50 views

Given $f:E \to E$ and $f \circ f = f $. Prove that if $f$ is surjective or injective then $f= Id_E$

asked Jan 19, 2022 at 14:19

0 votes

2 answers

59 views

Prove that if $I$ and $J$ are open intervals and $(I\cap \mathbb{Q}) \cap (J \cap \mathbb{Q}) = \emptyset$ then $I\cap J = \emptyset$.

asked Jan 21, 2022 at 15:09

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26 Questions

Prove that $f( \limsup \limits_{x \to +\infty} x_n)$ = $ \limsup \limits_{x \to +\infty} f(x_n)$ [closed]

Find the limit of $(1+\frac{1}{n^2})(1+\frac{2}{n^2})...(1+\frac{n}{n^2})$.

How to solve $\lfloor x \rfloor + \lfloor \frac{1}{x} \rfloor = 1$?

Question about the proof that if x is a real number then there exists a postive integer n such that -n < x < n. [closed]

How can I find the sup and inf of $m/n$ such that m,n are natural numbers and $m<2n$?

I don't know if my solution to a supremum problem is correct

A strange way to prove that $\lim_{x \to \infty} \sin(\frac{x^3}{x^2+1})$ does not exist.

A nice problem about convex functions and minimums.

Proving that $u_n = (1+ \frac{x}{n})^n$ is an increasing sequence for $n \in N$ and $n \geq |x|$.

If a function is not defined on all of its preimages set, can we talk about injectivity and surjectivity?

Find the limit of $u_n = \frac{1\times3\times5\times7\times..........\times(2n-1)}{2\times4\times6\times8\times........\times(2n)}$

How to integrate $\frac{\cos2x}{ \sin x + \sin 3x}$?

I am not sure whether my friend is saying the truth or if he's lying, how can I get the correct information out of him using logic?

Find the minimum average life of a hard disk

Can I prove the order limit theorem with a counter example? [closed]

An example of a linear map such that $Ker(f) \cap Im(f) \neq {0}$ and $f: R^2 \to R^2$ [duplicate]

What is the probability that a randomly chosen fetal heartrate differs from the mean by more than 25 bpm?

does the series $\sum | \frac{(-1)^n}{\sqrt{n}} (1+ \frac{(-1)^n}{\sqrt{n}}) |$ converge?

The limit of $ \frac{(x^2+y^2)^2}{x^2 - y^2} $ at the origin

Farthest and closest point in the circle $x^2 + y^2 = 80$ to the point (1,2)

What is the cardinality of $ \{ (A,B) \in \mathbb{P}(E)^2: A \subseteq B \}$ and $ \{ (A,B) \in \mathbb{P}(E)^2: A \cup B = E \}$

A question about the famous $\sum \frac{1}{\sqrt{n}}$ [duplicate]

How to prove the two subsequences $u_{2n}$ and $u_{2n+1}$ of the alternating harmonic series are adjacent?

Prove that if $ 0 \leq u_{n+1} \leq \frac{u_n + \epsilon_n}{K}$ then $\lim u_n = 0$.

Given $f:E \to E$ and $f \circ f = f $. Prove that if $f$ is surjective or injective then $f= Id_E$

Prove that if $I$ and $J$ are open intervals and $(I\cap \mathbb{Q}) \cap (J \cap \mathbb{Q}) = \emptyset$ then $I\cap J = \emptyset$.