8. El resultado de: \( \begin{array}{l}\text { A) }-6 \cos 6 x+C \\ \text { B) } 1 / 6 \cos 6 x+C \\ \text { C) }-1 / 6 \cos 6 x+C\end{array} \quad \int \operatorname{sen} 6 x d x \)

Calculate the maximum value of \( S \) if \( S=\frac{6}{x^{2}+2} \)

1. State whether the following statements are True or False. Justify your answer with the help of a short proof or a counter-example. No marks are awarded for a question without justification : \[ 2 \times 5=10 \] (i) The function \( f(x, y)=x y^{2} \quad \) satisfies Lipschitz condition on : \[ a \leq x \leq b,-\infty<y<\infty \]

Evaluate the derivative \( y=\sinh (x) \)

Use the intermediate value theorem to show that the function has a real zero between the two numbers given. Then, use your calculator to approximate the zer \( P(x)=4 x^{2}-2 x-6 ; 1 \) and 2 \( P(1)=\square \)

1) Integrer les equations suivante 1) \( y^{\prime}=\frac{1+y^{2}}{1+x^{2}} \) 2) \( y^{\prime \prime}-3 y^{\prime}+2 y=x^{2}-3 x \)