Known-a-R-and-function-f-R-R-satiesfied-xf-x-a-lt-sin-2-x-a-For-all-x-R-value-of-lim-x-a-f-x-

Question Number 55639 by gunawan last updated on 01/Mar/19

Known a \in R and

function f : R \to R satiesfied

∣ x f (x) + a ∣ < \sin^{2} (x - a) .

For all x \in R

value of \lim_{x \to a} f (x) . .

Answered by kaivan.ahmadi last updated on 01/Mar/19

- {s i n}^{2} (x - a) < x f (x) + a < {s i n}^{2} (x - a)

b y s a n d w i c h t h e o r e m

l i \underset{x \to a}{m x f} (x) + a = 0 \Rightarrow l i \underset{x \to a}{m} x f (x) = - a \Rightarrow

l i \underset{x \to a}{m x} \times l i \underset{x \to a}{m f} (x) = - a \Rightarrow

l i \underset{x \to a}{m f} (x) = - 1