## All Tasks

#### Intersection of two linear functions

Determinate the intersection point of the two linear functions:
$f(x)=-1,5x-1\\ g(x)=3x+8$.

# Linear functions

Training

8

#### An equation with functions

Let $f(x)=xe^x$.
Which $x\in\mathbb{R}$ solves the equation
$f'(x)-f(x)=0$?

# Exponential function

Reasoning

10

#### Study of horizontal asymptote

Let the function
$f(x)=\frac{e^x+x}{e^x}$,
we can say that

# Exponential function

Training

11

#### Comparison of functions

Are
$f(x)=\log_2{\frac{4x^2-2x}{2x-1}}$
and
$g(x)=1+\log_2x$
the same function?

# Logarithmic function

Reasoning

11

#### Fall Time of a Stone

About the previous task, $v(t) = 2,5 (1 - e^{-0,1t})$ after what amount of time is the stone sinking with a velocity of $2 m/s$?

# Parametric functions

Modeling

11

#### Calculating Natural Logarithm

Solve the following equation: $e^ {x+2}=21$. The result shall be rounded to three places to the right of the decimal point.

# Logarithm properties

Training

11