Dlketahui \( D=\frac{5}{4} r^{3} \hat{a}_{r} \) dimana \( r \leq 5 \leq 2 m ; 0 \leq z \leq 10 ; 0 \leq \varphi \leq 2 \pi \) Tunjukan ruas kiri dan kanan dari teorema divergensi \( / / \vec{D} \cdot \overrightarrow{d s}=/ / / / \nabla \cdot D \cdot d v \)

Determine the interval(s) on which the following function is continuous. \( f(x)=\frac{x^{2}-8 x+15}{x^{2}-9} \) The function is continuous on the interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to sepa

Suppose that \( f(x, y)=x^{4}+y^{4}-x y \). Then the minimum value of \( f(x, y) \) is.. A. -0.125 B. 0.125 C. 0 D. None of these answers

Find the derivative of the following function. \( g(t)=4 \sqrt{t} \) \( g^{\prime}(t)=\square \)

Find the intervals on which \( f \) is increasing and the intervals on which it is decreasing. \( f(x)=\frac{x^{4}}{4}-3 x^{3}+9 x^{2} \)

Find the derivative of the following function by first expanding the expression. \[ f(x)=(6 x+1)\left(5 x^{2}+7\right) \] \( f^{\prime}(x)=\square \)