\( \left\{ \begin{array} { l } { f ( x ) = \frac { \ln x - 1 } { \ln x } ; x > 0 } \\ { f ( 0 ) = 0 } \end{array} \right. \)

By using Newton-Raphson Method, determine the root for \( x^{3}+2 x^{2}-1=0 \). Given \( x_{0}=0.5 \). Give the answer correct to four decimal places. Dengan mengomenan

Show that \( F(x)=|x| \) is continuous everywhere.

USing first principle prove that \( y=\sin x \) then \( \frac{d y}{d x}=\cos x \)

11. Find the values of \( a \) and \( b \) that make \( f \) continuous everywhere. \[ f(x)=\left\{\begin{array}{ll}\frac{x^{2}-4}{x-2} & \text { if } x<2 \\ a x^{2}-b x+3 & \text { if } 2 \leq x<3 \\ 2 x-a+b & \text { if } x \geq 3\end{array}\right. \]

\( \lim _ { x \rightarrow 0 } \frac { 3 ( x - \operatorname { cts } x ) } { x } \)