All Tasks
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
Derivatives using arccotan
The derivative of the function $f(x)=2\text{arccot}(x+1)$ is:
# Functions of one variable
Training
13
Derivation arccotan
Let $ \displaystyle f(x)= \pi -\dfrac{b}{3}arccot(2x)$ with $b \in \mathbb{R}$, and let $f^{\prime}(x)$ and $f^{\prime\prime}(x)$ be the first and the second derivative of the function $f$.
Knowing that $\displaystyle f\left(\dfrac{\sqrt{3}}{2}\right) \cdot \dfrac{\sqrt{3} f^{\prime}\left(\dfrac{\sqrt{3}}{2}\right)}{2f^{\prime\prime}\left(\frac{\sqrt{3}}{2}\right)} = \dfrac{\pi}{4}$, then the value of $b$ is:
# Complements of differential calculus in real numbers
Training
13
Derivation arccotan
Let $f$ and $g$ be two differentiable functions in their domain, such that:
$f(x)= \dfrac{\pi}{2} -\dfrac{1}{3}arccot(2x-1)$ and $g(x)=\left( x^2+x+2\right) f(x)$.
Considering that $g^{\prime}(x)$ is the first derivative of function $g(x)$, then $g^{\prime}\left(0\right)$ is:
# Complements of differential calculus in real numbers
Training
13
Trigonometric equation
Solve the following trigonometric equation:
$3arccot(x − \sqrt{3})− \pi=0$
# Functions of one variable
Training
13