Verified answer

With no n in the formula we can ignore the n = 2, 4, and 8, so

sin x, 0 ≤ x ≤ π has a minimum of 0 at 0 and π, and a maximum of 1 at π/2, so

f(x) = 2 + sin x, 0 ≤ x ≤ π has a minimum of 3 at 2 and π, and a maximum of 3 at π/2.

The gist of the communicate available (sorry, there are too many pages to grant each and all of the hyperlinks) is that wands help to concentration the magic resident interior the witch or wizard, yet wandless magic continues to be obtainable, extremely for extremely proficient human beings like Snape and Dumbledore. some examples ... Apparition Assuming one's Animagus kind (or Metamorphpagus) Accio (the Summoning charm) Elves can do magic without making use of wands Lumos