Graph the folowing. State the parent function, transformations, domain and range

Can asymptotes be curved?
When I was first introduced to the idea of an asymptote, I was taught about horizontal asymptotes (of form y=a) and vertical ones ( of form x=b).
I was then shown oblique asymptotes-- slanted asymptotes which are not constant (of the form y=ax+b).
What happens, though, if we've got a function such as
$f(x)=e^x+\frac{1}{x}?$
Is $y=e^x$ considered an asymptote in this example?
Another example, just to show you where I'm coming from, is
$g(x)=x^2+\sin (x)$
-- is $y=x^2$ an asymptote in this case?
The reason that I ask is that I don't really see the point in defining oblique asymptotes and not curved ones; surely, if we want to know the behaviour of y as $x\to \mathrm{\infty }$, we should include all types of functions as asymptotes.
If asymptotes cannot be curves, then why arbitrarily restrict asymptotes to lines?

What is the distance between the following polar coordinates?:
${\displaystyle (11,\frac{17\pi }{12}),(4,\frac{\pi }{8})}$

Trigonometric integral Evaluate the following integrals.
${\displaystyle \int {\sin }^{2}0{\cos }^{5}0d0}$

From a proof of Simpson's rule using Taylor polynomial where $f\in [x_0,x_2]$ and, for
$x_1=x_0+h$
where
$h=\frac{x_2-x_0}{2}$
it got:
${\int }_{x_0}^{x_2}f(x)dx\cong 2hf(x_1)+h^3\frac{f^{″}(x_1)}{3}+h^5\frac{f^{(4)}(\xi )}{60}$
and then, it changed $f^{″}(x_1)$ by
$\frac{f(x_0)-2f(x_1)+f(x_2)}{h^2}$
Where it came?

Write the integral in terms of u and du. Then evaluate: ${\displaystyle \int {(x+25)}^{-2}dx,u=x+25}$

Find all rational zeros of the polynomial, and write the polynomial in factored form.
${\displaystyle P\left(x\right)=4x^3-7x+3}$

Compute $\int e^t\sqrt{9e^{2t}+4}dt$.