## All Tasks

#### Tangent and normal line of arccos

Let $f$ and $g$ be two differentiable functions in their domain, such that:
$g(x)=-3\pi +2 \arccos(3f(x)+1)$,
$f(1)=-\dfrac{1}{3}$ and $f^{\prime}(1)=\dfrac{2}{3}$.
The reduced equation of the tangent line to the graph of $g$ at the point with abscissa $1$ is:

# Complements of differential calculus in real numbers

Training

13

#### Arctan normal line

At the point of intersection with the ordinate axis, an equation of the straight line normal to the graph of the function $g(x)=2\arctan(x-1)$ is

# Functions of one variable

Training

12

#### Arctan slope normal line

Consider the curve $g(x)=\frac{4\arctan(x+1)}{\pi}$ and the point $P(0,1)$. Find the slope of the normal line to the graph of $g$ at $P$.

# Functions of one variable

Learning

13

#### Identities & Algebraic expression_1

Simplfy the following expression:
$A=(x-2)^2-x^2$ and then identify the correct statements

# Linear equations

Reasoning

9

#### Identities & Algebraic expression_2

Simplfy the following expression:
$\frac{{(2x-3)}^2-4(x-2)(x+2)+x(x^2+15)-25}{x^2+3}$ and then identify the correct statements

# Equations & Inequations

# Polynomial functions

Reasoning

9

#### Identities & Algebraic expression_3

Simplfy the following expression:
$A=(x-y)^2-(x^2+4)$ and then identify the correct statements

# Equations & Inequations

Reasoning

9