Q3, 2,6 ball) Moddiy nuqta \( s(t)=-\frac{t^{5}}{5}+12 t^{2} \) qonuniya bilan harakatlanmoqda \( (s(t) \) metrda, t sekundda o'lchana \( t_{0}=2 \) sekunddagi oniy tezligi qiymatini toping.

(c) Use Bisection method to solve \( x^{3}-9 x+1=0 \) for the root between \( x=2 \) and \( x=4 \). 5 marks) (d) Using \( \sin (0.1)=0.09983 \) and \( \sin (0.2)=0.198 \), find an appropriate value of \( \sin (0.15) \) by using Langranges interpolation.

4. For which values of \( x \) will \( \sum_{k=1}^{\infty}(4 x-1)^{k} \) exists.

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } ( \frac { \sin x } { x } ) } \\ { \left. \begin{array} { l | l | l | } \hline & { - 0.001 } & { 0 } \\ { F ( x ) } & { 0.001 } \\ \hline \end{array} \right. } \end{array} \right. \)

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } ( \frac { \sin x } { x } ) } \\ { \left. \begin{array} { l | l | l | l | } { x } & { - 0.001 } & { 0 } & { 0.001 } \\ \hline f ( x ) & { } & { } & { } \\ \hline \end{array} \right. } \end{array} \right. \)

6. \( \lim _{x \rightarrow 2}\left(\frac{x^{2}-5 x+6}{x-2}\right) \) \begin{tabular}{l|l|l|l|l|}\( x \) & 1.99 & 1.999 & 2 & 2.001 \\ \hline\( f(x) \) & & & & \\ \hline\end{tabular}