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. \( I=\frac{9}{2}\left(e^{4}+1\right) \)

Given the following function, determine the difference quotient, \( \frac{f(x+h)-f(x)}{h} \) \[ f(x)=x^{2}-7 x+3 \] Answer

Derivative DF \( F(x)=\frac{x}{\sqrt[3]{x^{2}+4}} \)

Differentiate. \( F(x)=\frac{1}{9 x-7} \)

Determine the implied domain of the following function. Express your answer in interval notation.

On considère la fonction numérique \( f \) définie par : \[ f(x)=x-\sqrt{3-x^{2}} \] 1. Determiner \( D f \). \( \forall x \in D_{f} \quad f(x) \geq-2 \sqrt{3} \). 2. Montrer que : il la valeur minimale de \( f \) sur \( D_{f} \).