A curve has equation \[ y=x^{3}+p x^{2}+q x-45 \] The curve passes through point \( R(2,3) \) The gradient of the curve at \( R \) is 8 (a) Find the value of \( p \) and the value of \( q \).

\( \int _ { 2 } ^ { 5 } \int _ { 0 } ^ { \pi / 2 } r \cos \theta r \sin \theta d \theta d r = \)

\( f : R ^ { 2 } \rightarrow R , f ( x , y ) = 2 x ^ { 2 } + 3 x y + 4 y ^ { 2 } - 5 x + 2 y + 2024 \)

\( F ( x ) = \int _ { x } ^ { x ^ { 2 } } e ^ { t ^ { 7 } } d t \)

Soit \( f \) la fonction définie sur \( \mathbb{R}^{+} \operatorname{par} f(x)=\frac{2 \sqrt{x}}{x+1} \) Monter que \( f \) est majoréeqar 1. \( f \) est-elle bornée? Justifier votre réponse.

find the easiest solution, please: 1) \( \frac{\lim _{2}}{\frac{x^{5}}{\sqrt[3]{x+6}-64}} x \)