All Tasks - Asymptote

Let $f(x)= \dfrac{\pi}{2} -2 \arcsin(1-2x)$ with domain $D_f = \left[0, 1\right]$. The reduced equation of the line normal to the graph of $f$ at the point with abscissa $\dfrac{1}{4}$ is:

Let $y=y(x)=\arccos(1-5x)$ and $x=x(t)=\frac{1}{5}+ln(3t^2-2)$. Using the chain rule formula to express the derivative $\left.\frac{dy}{dt}\right|_{t=1}$.

Compute the value of $x$ that satifies the equation \[6\arcsin\left(x+7\right)-4\;\text{arccot}(-1)=0\]

Consider the following functions: \[f_1(x)=\arccos\left(-\frac{x}{4}\right)-\frac{\pi}{4}\] \[f_2(x)=\frac{\pi}{4}+\arctan(2x)\] \[f_3(x)=\frac{\pi}{4}-\arcsin\left(\frac{x}{4}\right)\] \[f_4(x)=\text{arccotan}(2x)-\frac{\pi}{4}\] Match each function with its respective graph shown in the figure.

Let $f$ be a diferentiable function in $\mathbb{R}$ and $g(x)=f(\pi/2+\arcsin(2x-1))$. Find the derivative of $g$ at the point where the line $2x-2y=1$ intercepts The $x$ axis.

How heavy is the boy?