C | math4u.vsb.cz

1003034402

Level:

In a class of

31

pupils,

18

pupils learn Italian,

16

pupils learn Spanish and

12

pupils learn Portuguese. Now,

7

pupils learn Italian and Spanish,

9

pupils learn Italian and Portuguese and

5

pupils learn Spanish and Portuguese. Finally,

3

students do not learn any of these three languages. How many pupils learn all these languages?

3

5

2

1

1003034401

Level:

There are

47

students in a class. Among these students

22

are members of a sports club,

33

are members of a film club and

20

students joined a literary club. Further,

17

students are members of the sports club and the film club,

13

joined the film club and the literary club,

6

attend the sports club and the literary club. Only one student is a member of all the clubs. How many students from the class attend neither the sports club nor the literary club?

11

7

36

4

1003047610

Level:

Find the limit

lim_{n \to \infty} \frac{\sqrt{4 n + 5}}{\sqrt{2 n^{3} + 3 n^{2} - 1}}

0

\sqrt{2}

2

\infty

- 5

1003047609

Level:

Find the limit

lim_{n \to \infty} \frac{\sqrt{4 n^{2} + 3 n + 1}}{\sqrt{2 n^{2} - 5 n - 7}}

\sqrt{2}

2

- \frac{1}{7}

0

\infty

1003047608

Level:

Choose the step to take first to efficiently evaluate the limit of the sequence

{(\frac{3 n + 2}{\sqrt{n^{2} - 1}})}_{n = 1}^{\infty}

We divide the numerator and the denominator by

n

We take

\sqrt{n}

outside brackets in the numerator and the denominator.

We square the denominator.

We divide the numerator by

n

We divide the denominator by

n

1003047607

Level:

Find the limit

lim_{n \to \infty} n (\sqrt{n} - \sqrt{n - 1})

\infty

\frac{1}{2}

0

2

- \infty

1003047606

Level:

The sequence

{(\sqrt{n} (\sqrt{n} - \sqrt{n - 1}))}_{n = 1}^{\infty}

is:

convergent and

lim_{n \to \infty} \sqrt{n} (\sqrt{n} - \sqrt{n - 1}) = \frac{1}{2}

convergent and

lim_{n \to \infty} \sqrt{n} (\sqrt{n} - \sqrt{n - 1}) = 0

convergent and

lim_{n \to \infty} \sqrt{n} (\sqrt{n} - \sqrt{n - 1}) = 2

divergent and

lim_{n \to \infty} \sqrt{n} (\sqrt{n} - \sqrt{n - 1}) = \infty

divergent and it does not have an infinite limit

1003047605

Level:

Find the limit

lim_{n \to \infty} (\sqrt{n} - \sqrt{n - 1})

0

\infty

- \infty

- 1

\sqrt{2}

1003047604

Level:

Choose the correct computation of the limit.

L = lim_{n \to \infty} (\sqrt{n^{2} + 3 n} - 2 n)

L = lim_{n \to \infty} n (\sqrt{1 + \frac{3}{n}} - 2) = - \infty

L = \infty - \infty = 0

L = lim_{n \to \infty} (n - 2 n) = - \infty

L = lim_{n \to \infty} (n^{2} + 3 n - 4 n^{2}) = - 3

L = lim_{n \to \infty} \frac{n^{2} + 3 n - 4 n^{2}}{\sqrt{n^{2} + 3 n} + 2 n} = \infty

1003047603

Level:

Find the limit

lim_{n \to \infty} (\sqrt{4 n^{2} + 3 n} - 2 n)

\frac{3}{4}

\infty

0

- \infty

\sqrt{2}

C

1003034402

1003034401

1003047610

1003047609

1003047608

1003047607

1003047606

1003047605

1003047604

1003047603

Events

Akce

Interests

Zajímavosti

About portal

O portálu