All Tasks

A problem of one euro

A 1 euro coin is made of a bimetallic layered composition: cupronickel for the silver part (internal) and brass for the gold part (external). The euro has a 23.25 mm diameter. What is the radius of the inner circumference if the distance between the golden (outer) and silver (inner) circumferences is d = 3 nm?
 
# Circle

Training
5

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.
 
# Unassigned

7

Differential_arctan_B_T

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_A_T

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_I_T

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:
 
# Unassigned

Training
13

IFDT_arctan_B_T_2

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