All Tasks

Values of inverse trigonometric functions

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

Training
13

Graphs - Inverse trigonometric functions

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.
 
# Functions of one variable

Reasoning
13

Chain rule arcsin

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.
 
# Functions of one variable

Reasoning
13

Scale balance

How heavy is the boy?
 
# Unassigned

Modeling
9

Side length of a rectangle

Which of the following equations fits the picture if the goal is to calculate the length of x?
 
# Unassigned

Reasoning
9

Differential of the function arcsin

Find the differential of the function $y=\arcsin(\frac{u}{v})$ where $u$ and $v$ are differentiable functions of $x$.
 
# Functions of one variable

Training
13