let-f-x-cosx-1-x-1-prove-that-f-x-1-x-2-x-2-8-x-0-2-ptove-that-f-x-2-pi-e-1-x-1-ln-cosx-x-pi-2-

Question Number 66322 by mathmax by abdo last updated on 12/Aug/19

l e t f (x) = {(c o s x)}^{\frac{1}{x}} (1) p r o v e t h a t f (x) \sim 1 - \frac{x}{2} + \frac{x^{2}}{8} (x \to 0)

(2) p t o v e t h a t f^{^{'}} (x) \sim - \frac{2}{π} e^{(\frac{1}{x} - 1) l n (c o s x)} (x \to \frac{π}{2})