الآنا
E2-4 مرحلة ثانية شعبة رانية إشعار واحد
Answer two questions only.
Q1: Solve the equation
$z^{4} = - 1 + i$
Q2: let $z = x y + \sin x$ . Find the total derivative.
Q3: Evaluate the double integral
$\iint_{R} (2 \frac{x^{2}}{y^{2}} + 2 y) d A$
Where $R : \begin{array}{l} 1 \leq x \leq 2 \\ 1 \leq y \leq x \end{array}$

Answer

Expert–verified

Hide Steps

Answer

$R : \begin{array}{l} 1 \leq x \leq 2 \\ 1 \leq y \leq x \end{array}$

Steps

Step 1 ：Q1:

Step 2 ： $z^{4} = - 1 + i$

Step 3 ：Q2:

Step 4 ： $z = x y + \sin x$

Step 5 ： $\frac{d z}{d t} = \frac{\partial z}{\partial x} \frac{d x}{d t} + \frac{\partial z}{\partial y} \frac{d y}{d t}$

Step 6 ：Q3:

Step 7 ： $\iint_{R} (2 \frac{x^{2}}{y^{2}} + 2 y) d A$

Step 8 ： $R : \begin{array}{l} 1 \leq x \leq 2 \\ 1 \leq y \leq x \end{array}$