b) Montrer que : \( \lim _{x \rightarrow+\infty} f(x)=+\infty \) puis calculer \( \lim _{x \rightarrow+\infty} \frac{f(x)}{x} \)

What is the solution to the following differential equation, subject to the initial condition \( y(0)=2 \) ? \( \frac{d y}{d x}=6 x+6 \)

\( \int _ { 0 } ^ { 2 } \int _ { 0 } ^ { y } \frac { d x d y } { ( x + y ) ^ { 3 } } \)

\( \lim _{x \rightarrow +\infty } (x+\frac{1}{x}-\ln (x)^{2}-2) \)

Determine the area bounded by the functions \( y = \sin(x) \) and \( y = \cos(x) \) within the interval \( [0, \frac{\pi}{2}] \).

What is the limit of the following? \( \lim _{x \rightarrow-\infty} \frac{-2 x^{2}+3 x-4}{3 x^{2}-2 x-1} \)