## All Tasks

#### Chain rule arcsin

Determine the equation of the normal line to the graph of $y(x)=6\arcsin(f(x))$ at $x=0$, knowing that $f(0)=0.5$ and $f'(0)=1$

# Functions of one variable

Reasoning

13

#### Differential - approximate arcsin

Use differential to approximate the change in
$y=\arcsin(1-x)$ when $x$ changes from $1$ to $0.95$.

# Functions of one variable

Reasoning

13

#### Translation of the verbal expression into algebraic expression_1

The following verbal expression:
In a number we add five and then we add the triple of him.
The translation of this verbal expression into an algebraic expression is:

# Terms with variables

Reasoning

8

#### Overtime

Kev and Doug are drivers of a parcel service.
Last month Kev get 875€ extra for 35 hours overtime working during a month. Calculate how many money Doug get in that month for 24 h overtime working, when he get the same money per hour.

# Direct proportionality & rule of three

Modeling

8

#### Inverse function derivative theorem arcsin

Consider $y=f(x)= \dfrac{\pi}{2} -2 \arcsin(1-2x)$ with domain $D_f=\left]0, 1 \right[ $.
Applying the inverse function derivative theorem, the expression of $\dfrac{dx}{dy}$ is:

# Complements of differential calculus in real numbers

Training

13

#### Inverse function derivative theorem arcsin

Consider $y=f(x)= 2 \arcsin\left(\dfrac{x}{3}\right)$ with domain $D_f=\left]-3, 3 \right[ $.
Applying the inverse function derivative theorem, the expression of $\dfrac{dy}{dx}$ is:

# Complements of differential calculus in real numbers

Training

13