I'm supposed to find asymptotes for x⋅arctan(x) for a homework assignment. Are there any theorems regarding this I can utilize to find the equation for the asymptotes, or is this one of those solve case by case things, where this particular equation can be solved in some neat way, but there is no easy universal way to find asymptotes like this? I know it should be: +- pi/2 x−1 but "how do I show this?" is essentially my question. Thanks in advance

What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1)?

How to expand and simplify ${\displaystyle 2(3x+4)-3(4x-5)}$?

Find an equation equivalent to $x^2-y^2=4$ in polar coordinates.

How to graph ${\displaystyle r=5\sin \theta }$?

How to find the length of a curve in calculus?

When two straight lines are parallel their slopes are equal.
A)True;
B)False

Integration of 1/sinx-sin2x dx

Converting percentage into a decimal. $8.5\%$

Arrange the following in the correct order of increasing density.
Air
Oil
Water
Brick

What is the exact length of the spiraling polar curve ${\displaystyle r=5e^{2\theta }}$ from 0 to ${\displaystyle 2\pi }$?

What is ${\displaystyle \frac{\sqrt{7}}{\sqrt{11}}}$ in simplest radical form?

What is the slope of the tangent line of ${\displaystyle r=-2\sin \left(3\theta \right)-12\cos \left(\frac{\theta }{2}\right)}$ at ${\displaystyle \theta =\frac{-\pi }{3}}$?

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

Use the summation formulas to rewrite the expression ${\displaystyle \Sigma \frac{2i+1}{n^2}}$ as i=1 to n without the summation notation and then use the result to find the sum for n=10, 100, 1000, and 10000.

How to calculate the right hand and left hand riemann sum using 4 sub intervals of f(x)= 3x on the interval [1,5]?