## All Tasks

#### Integral using variable change

Using the change of variables $u=e^x$, the integral
$$\int\frac{1}{e^x+1}dx$$ is:

# Integration calculus

Learning

13

#### Primitive concept

Without solving the integral tell if the equality is true (T) or false (F)
$\int \frac{\sin(x)}{cos^2(x)}dx=\sec(x)+C$

# Integration calculus

Reasoning

13

#### Primitive concept

Without solving the integral tell if the equality is true (T) or false (F)
$\int x\sin(x)dx=x \cos(x)-\sin(x)+C$

# Integration calculus

Training

13

#### Support for finding out of hypotenuse

Which one of the sides is the hypotenuse?

# Pythagorean theorem

Training

9

#### The top-right diagonal

Likewise, looking at this spiral of numbers, find the few first items along the diagonal, beginning with 4, 16, 36,...

# Sequences

# Natural numbers

Modeling

5

#### What is bigger?

Consider the unit squares in the infinite square lattice in the plane on one side, and the integer numbers, as well infinitely many of them, on the other side. What can you say about them?

# Set theory

Modeling

13