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mmmmh mmmmmh
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4 votes
1 answer
89 views

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

3 votes
1 answer
178 views

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

3 votes
4 answers
125 views

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

2 votes
0 answers
51 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]

2 votes
2 answers
588 views

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

1 vote
0 answers
59 views

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

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.

1 vote
0 answers
47 views

A nice problem about convex functions and minimums.

1 vote
1 answer
67 views

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

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?

1 vote
1 answer
67 views

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

1 vote
3 answers
66 views

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

1 vote
1 answer
128 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?

1 vote
1 answer
65 views

Find the minimum average life of a hard disk

1 vote
2 answers
69 views

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

1 vote
0 answers
47 views

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

0 votes
1 answer
73 views

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

0 votes
1 answer
85 views

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

0 votes
1 answer
80 views

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

0 votes
1 answer
872 views

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

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 \}$

0 votes
0 answers
52 views

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

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?

0 votes
0 answers
16 views

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

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 $f= Id_E$

0 votes
2 answers
60 views

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