The angular speed of a point on a planet is \( \frac{7 \pi}{10} \) radian per hour. The equator lies on a circle of radius approximately 8000 miles. Find the linear velocity, in miles per hour, of a point on the equator. The linear speed of a point on the equator is approximately \( \square \) miles per hour.

\[ f^{\prime \prime}(x)=\frac{4}{x^{3}} \] etudiar la concuvite

\( y = \ln \quad | \sec 2 x ^ { 3 } | \)

\( y ^ { \prime } + y = x \sqrt[ 3 ] { y ^ { - 2 } } \)

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

\( \lim _ { h \rightarrow 0 } \frac { ( x + n ) ^ { 2 } - x ^ { 2 } } { h } \)