Question

Really need help understanding this limit/derivative question...
The limit
Lim x approachs 5pi CosX +1 / x-5pi


represents the derivative of some function f(x) at some number a. Find f and a .

I don't even understand the wording of this question...

Answer 1

There is an alternative form for the definition of a derivative...\[f'(a)=\lim_{x \rightarrow a} \frac{f(x)-f(a)}{x-a}\]It is often used when your are analyzing a piecewise defined function where the continuity is questionable.
If we re-write your problem to fit this form...\[f'(5\pi)=\lim_{x \rightarrow 5\pi} \frac{f(x)-f(5\pi)}{x-5\pi}\]If f(x) is the cosine...\[f'(5\pi)=\lim_{x \rightarrow 5\pi} \frac{\cos (x)-\cos (5\pi)}{x-5\pi}\]From this, it looks like f(x)=cos(x) and a=5pi .