All Tasks
Scale balance
How heavy is the boy?
# Terms with variables
# Systems of linear equations
Modeling
9
Side length of a rectangle
Which of the following equations fits the picture if the goal is to calculate the length of x?
# Linear equations
# Square & rectangle
Reasoning
9
Differential of the function arcsin
Find the differential of the function $y=\arcsin(\frac{u}{v})$
where $u$ and $v$ are differentiable functions of $x$.
# Functions of one variable
Training
13
Derivation rules arcsin
Let $ \displaystyle f(x)= a -2 \arcsin(1-2x)$ with $a \in \mathbb{R}$ and let $f'(x)$ and $f''(x)$ be the first and the second derivative of a function $f$.
Knowing that $\displaystyle \dfrac{f\left(\dfrac{1}{2}\right)}{f'\left(\dfrac{1}{2}\right)} + f''\left(\frac{1}{2}\right) = 2$, then the value of $a$ is:
# Functions of one variable
Training
13
Tangent and normal lines
The figure shows :
- part of a function $f$
- a line $r$ tangent to the graph of $f$ at the point with abscissa iqual to $2$
The value of $f'(2)$, derivative of the function $f$ at the point of abscissa $2$, can be equal to:
# Functions of one variable
Reasoning
13
Derivation rules arcsin
Consider $f(x)= 2 \arcsin\left(\dfrac{x}{3}\right)$ with domain $D_f=[-3, 3]$.
Let $f'(x)$ be the first derivative of function $f(x)$, then $f'\left(1\right)$ is:
# Functions of one variable
Training
13