8. \( \lim _{x \rightarrow 0} \frac{e^{3+x}-e^{3}}{x} \) 10. \( \lim _{x \rightarrow 0} \frac{e^{\sin x}-1}{x} \)

3. \( h(x)=x^{2}+5 x-2 \) \( \frac{d h(x)}{d x}=\lim _{\Delta x \rightarrow}=\frac{h(x+\Delta x)-h(x)}{\Delta x} \)

Calcular \( y^{\prime}=\frac{d y}{d x} \) de la función implicita \( \frac{x^{2}}{4}+\frac{x^{2}}{9}=3 x y \) y simplificar:

\( \left. \begin{array} { l } { f ( x ) = - x ^ { 4 } - 3 x ^ { 3 } } \\ { h ( x ) = - 2 ( x - 2 ) ^ { 2 } ( x + 2 ) } \end{array} \right. \)

3. \( h(x)=x^{2}+5 x-2 \) \( \frac{d h(x)}{d x}=\lim _{\Delta x \rightarrow 0}=\frac{h(x+\Delta x)-h(x)}{\Delta x} \)

18. Fie funcția \( f: R \rightarrow R, f(x)=e^{x} \cdot\left(a x^{2}+b x+c\right) \). Determinaţi numerele reale \( a, b \) şi \( c \), ştiind că \( f(0)=0, f^{\prime}(0)=1 \) şi \( f^{\prime \prime}(0)=4 \).