10 The diagram shows a right circular cone with radius 10 cm and height 30 cm . The cone is imitially completely fllled with water. Water leaks out of the cone through a small hole at the vertex at a rate of \( 4 \mathrm{~cm}^{-1} \mathrm{~s}^{-1} \). a Show that the volume of water in the cone. \( V \mathrm{~cm}^{3} \), when the height of the water is \( h \mathrm{~cm} \) is given by the formula \( V=\frac{\pi h}{27} \). b Find the rate of change of \( h \) when \( h=20 \).

Find the integral. \( \int x^{6} d x \)

Explique o Teorema Fundamental do Cálculo e como ele relaciona a diferenciação e a integração.

Find the integral. \( \int\left(x^{4}-2 x^{3}\right)^{4}\left(4 x^{3}-6 x^{2}\right) d x \) A. \( \frac{1}{5}\left(x^{4}-2 x^{3}\right)^{5}+C \) B. \( \frac{1}{4}\left(x^{4}-2 x^{3}\right)^{4}+C \) C. \( \left(x^{4}-2 x^{3}\right)^{5}+C \) D. \( 4 x^{3}-6 x^{2}+C \)

Approximate the area under the graph of \( f(x) \) and above the \( x \)-axis using \( n \) rectangles. \( f(x)=x^{2}+2 \); interval \( [0,5] ; n=5 \); use left endpoints A. 40 B. 32 C. 65 D. 66

91. \( f(\theta)=\frac{6\left(2-\theta^{3}\right)}{3-2 \theta} \)