All Tasks

Tangent line of the arccos

Determine the equation of tangent line of $\arccos(x)$ for $x=0.6$. The equation of the tangent line can be described by the function $t(x)=mx+b, m, b\in\mathbb{R}$. Insert the values of $m$ and $b$ in the related check boxes. Round to two decimal digits each.
 
# Complements of differential calculus in real numbers

Training
13

Equation inverse trigonometric and its derivatives

Find $x$ solution of the equation $$\frac{5}{2}-f'\left(\frac{4}{5}\right)-\arcsin(\sqrt{2}x)=f\left(\frac{4}{5}\right)$$ where $f$ is the function given by $f(x)=\text{arccot}(3-5x)-\pi$
 
# Functions of one variable

Training
13

Domain & Range of Arcsine

The graph of arcsine function is plotted in the picture in the range [-1, 1]. Take a look at it and mark the correct statements subsequently.
 
# Functions of one variable

Learning
13

Tangent line arccotan

Let $f$ be the function defined by $f(x) =2-arccot(2x)$. The slope of the tangent line to $f$ at the point with the ordinate equal to 2 is (enter the slope value to 2 decimal places)
# Functions of one variable
# Complements of differential calculus in real numbers

Training
13

Normal line of arccotan

Consider the function defined by $f(x)=4 arccot(x+1)$. Let $n$ be the normal line of $f$ for $x=0$ and let $A(-2\pi, k)$ one point of line $n$. Determine $k$.
 
# Functions of one variable

Training
13

Derivation arccotan

Consider $f(x)= 3arccot\left(2x-1\right)$ with domain $D_f=\mathbb{R}$. Let $f^{\prime}(x)$ be the first derivative of function $f(x)$, then $f^{\prime}\left(-\dfrac{1}{2}\right)$ is:
 
# Complements of differential calculus in real numbers

Training
13