All Tasks
Hexagonal prism
The decorative block around the statue of Prince Pribina has the shape of a hexagonal prism, the base of which is an irregular hexagon. The height of the prism is 21 cm. Calculate the sum of the lengths of all edges of this prism in centimetres. Measurements are in centimetres.
# Prism
Training
7
Differential Arctan
Consider the function $f(x)= -2 \arctan\left(2x\right)$ with domain $D_f = \mathbb{R}$.
The differential of the function $y=f(x)$ at the point $x=-\dfrac{1}{2}$ is:
# Complements of differential calculus in real numbers
Training
13
Approximate values arctan
Consider the function $f(x)= -2 \arctan\left(2x\right)$ with domain $D_f = \mathbb{R}$.
Using differentials, the approximate value of $\ -2 \arctan\left(0.02\right)$ is:
# Complements of differential calculus in real numbers
Training
13
Differential Arctan
Consider $f(x)= \dfrac{\pi}{2} -2 \arctan(1-2x)$ with domain $D_f=\mathbb{R} $.
Knowing that the value of $df(x_0)=4 \ dx$, the value of $x_0$, is:
# Complements of differential calculus in real numbers
Training
13
Arctan inverse function derivative theorem
Consider $y=f(x)= -2 \arctan\left(2x\right)$ with domain $D_f=\mathbb{R}$.
Applying the inverse function derivative theorem, the expression of $\dfrac{dx}{dy}$ is:
# Complements of differential calculus in real numbers
Training
13
Arctan inverse function derivative theorem
Consider $y=f(x)= -2 \arctan\left(2x\right)$ with domain $D_f=\mathbb{R}$.
Applying the inverse function derivative theorem, the expression of $\dfrac{dy}{dx}$ is:
# Complements of differential calculus in real numbers
Training
13