iran-konkur 2023 Q17

iran-konkur · Other · konkur-riazi_1402_general Chain Rule Limit Involving Derivative Definition of Composed Functions
17 -- If $f(x) = \left(\dfrac{-1+\sin x}{1+\sin x}\right)^2$ and $f(x) = xg(x)+1$, then $\displaystyle\lim_{x \to 0} g(x)$ equals:
(1) $4$ (2) $2$ (3) $-4$ (4) $-2$
\textbf{17 --} If $f(x) = \left(\dfrac{-1+\sin x}{1+\sin x}\right)^2$ and $f(x) = xg(x)+1$, then $\displaystyle\lim_{x \to 0} g(x)$ equals:

\medskip
(1) $4$ \hfill (2) $2$ \hfill (3) $-4$ \hfill (4) $-2$

\bigskip