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1 Some math

Based on the graph of the function f (x) = |x2− 5x + 6| we can determine the number of solutions of the equation f (x) = m, depending on the value of the parameter m.

It is known that lim

t→0

sin t

t = 1, so lim

x→π2

sin x −π2 x − π2 = 1.

A function ϕ : R → R is given by the formula

ϕ(x) = 3x2− 1+x2 4

8x6+ 1 sin3x + 1 8 . The numbers of the sequence (an) are of the form

an= 5n3+ 3n2− n 4n2+ 2n − 1

14

, n = 1, 2, . . . .

It is known that the number series

∞

P

n=1 1

n is divergent and the series

∞

P

n=1 1

(2n−1)2 is convergent and

∞

X

n=1

1

(2n − 1)2 = π2 8 .

1

(2)

2 Everyday matters

Here is the shopping list to make today:

1. baked products (a) bread;

(b) 5 rolls;

2. dairy products (a) milk;

(b) butter;

(c) yogurts;

3. printer paper;

4. pens (a) blue;

(b) black.

2

(3)

3 About me

My hobby:

• listening to music - performer X;

- performer Y;

- performer Z;

• sport

- jogging;

- cycling.

My favorite friends:

♥ Mag

♥ Zuza

♥ Aga

♥ Karol

♥ Robert

♥ Pablo

Contents

1 Some math 1

2 Everyday matters 2

3 About me 3

3

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