9/16/24, 1:31 \( P M \) 16. Find \( f^{\prime}(x) \) using the rules for finding derivatives, \( f(x)=\frac{6 x-2}{x-2} \) \( f^{\prime}(x)=\square \)

11. Sia data la funzione \( f \), derivabile in \( \mathbb{R} \), tale che \( f(0)=-5, f^{\prime}(0)=-4 \). Allora \( g(x)=|f(x)| \) a) \( g(x) \) presenta un punto angoloso in \( x=0 \) b) \( P(0,5) \in g(x) \) e \( g^{\prime}(0)=-4 \) c) \( g \) è derivabile in \( x=0 \) e \( g^{\prime}(0)=4 \) d) \( g \) è derivabile in \( x=0 \) e \( g^{\prime}(0)=-4 \) e) \( \lim _{x \rightarrow 0^{-}} g^{\prime}(x)=-4 ; \lim _{x \rightarrow 0^{+}} g^{\prime}(x)=4 \)

\( L ( \sinh ( a t + b ) ) \)

\( L ( \cos ( a t + b ) ) \)

In exercises 18 to 22 , find the limit, If the limit does not exist, justify your answe (18) Limit of the function \( f(x)=\frac{|x-3|}{x-3} \) as \( x \) tends to 3 )rom the right:

1. The integral \( \int_{\pi / 6}^{\pi / 3} \tan ^{3} x \cdot \sin ^{2} 3 x\left(2 \sec ^{2} x \cdot \sin ^{2} 3 x+3 \tan x \cdot \sin 6 x\right) d x \) \( \begin{array}{ll}\text { (1) } \frac{9}{2} & \text { (2) }-\frac{1}{9} \\ \text { (3) } \frac{7}{18} & \text { (4) }-\frac{1}{18}\end{array} \)