\( 2.3 x=3+\sqrt{x^{2}+y^{2}} \) 2.3.1. 2.3.2 Determine \( \frac{d y}{d x} \) Determine the equation of the tangent to the graph at point \( (4,3 \)

\( f^{\prime}(x)=\frac{x^{2}-4}{2 x^{2}} \) colculer \( f^{\prime \prime}|x| \)

\[ f^{\prime \prime}(x)=\frac{4}{x^{3}} \] etudiar la concuvite

\( f(x)=\left(x^{2}+1\right)^{2} \) es

Evaluate the double integral \[ I=\iint_{A} 18 y e^{x^{2}} d x d y \] when \( A \) is the region in the first quadrant bounded by the graphs of \[ x=y^{2}, \quad x=2, \quad y=0 \] 1. \( I=18\left(e^{4}+1\right) \) 2. \( I=\frac{9}{2}\left(e^{4}-1\right) \) 3. \( I=9\left(e^{4}-1\right) \) 4. \( I=\frac{9}{2} e^{4} \) 5. \( I=\frac{9}{2}\left(e^{4}+1\right) \)

a) \( \lim _{x \rightarrow-2} \frac{x^{2}+3 x+6}{(x+2)^{2}} \)