Consider the function \( f(x) \) whose second derivative is \( f^{\prime \prime}(x)=10 x+8 \sin (x) \). If \( f(0)=3 \) and \( f^{\prime}(0)=4 \), what is \( f(3) \) ?

\( f ( x ) = \frac { x + 10 } { x - 4 } \quad D f = ? \)

8. \( \lim _{x \rightarrow 4} \frac{\sqrt{3 x-3}-3}{2-\sqrt{x}} \) Ans.: -2

(2) Nontrer que la forme implicite de la solution de l'ED \( 9 y y^{\prime}+4 x=0 \) est \( \frac{x^{2}}{9}+\frac{y^{2}}{4}=k \) (cste)

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

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 : \[ a \leq x \leq b,-\infty<y<\infty \]