All Tasks
Solving linear equation 1
Solve the linear equation by equivalent transformation.
7x + 22 = 71
# Unassigned
Training
7
Tangent and normal line of arccos
Let $f$ and $g$ be two differentiable functions in their domain, such that:
$g(x)=-3\pi +2 \arccos(3f(x)+1)$,
$f(1)=-\dfrac{1}{3}$ and $f^{\prime}(1)=\dfrac{2}{3}$.
The reduced equation of the tangent line to the graph of $g$ at the point with abscissa $1$ is:
# Complements of differential calculus in real numbers
Training
13
Arctan normal line
At the point of intersection with the ordinate axis, an equation of the straight line normal to the graph of the function $g(x)=2\arctan(x-1)$ is
# Functions of one variable
Training
12
Arctan slope normal line
Consider the curve $g(x)=\frac{4\arctan(x+1)}{\pi}$ and the point $P(0,1)$. Find the slope of the normal line to the graph of $g$ at $P$.
# Functions of one variable
Learning
13
Identities & Algebraic expression_1
Simplfy the following expression:
$A=(x-2)^2-x^2$ and then identify the correct statements
# Linear equations
Reasoning
9
Identities & Algebraic expression_2
Simplfy the following expression:
$\frac{{(2x-3)}^2-4(x-2)(x+2)+x(x^2+15)-25}{x^2+3}$ and then identify the correct statements
# Unassigned
Reasoning
9