A formula for the derivative of a function \( f \) is given. How many critical numbers does \( f \) have? \[ f^{\prime}(x)=\frac{100 \cos ^{2}(x)}{10+x^{2}}-1 \] 4 \( x \quad \) critical numbers

\( \lim _ { x + \infty } [ \sqrt { x ^ { 2 } + 2 x } - ( x + 1 ) ] \)

\( \frac { \sqrt[ 3 ] { ( ( x _ { 0 } + \Delta x ) - 1 ) ^ { 2 } + \sqrt[ 3 ] { ( x _ { 0 } - 1 ) ^ { 2 } } } } { \Delta x \cdot ( \sqrt[ 3 ] { x _ { 0 } - 1 } + \sqrt[ 3 ] { x _ { 0 } - 1 } ) } \)

Determine the volume generated by revolving the area between \( y = \sqrt{x} \) and the x-axis from \( x = 0 \) to \( x = 4 \) about the y-axis with the washer method.

\( \lim _ { x \rightarrow 9 } ^ { 9 : 03 } ( \frac { \sqrt { x - 9 } } { \sqrt { x } - 3 } ) \)

\( \int \int _ { s } f ( x , y , z ) d s = \int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 2 \pi } f ( s ( \phi , \theta ) ) \| \frac { \partial s } { \partial \phi } \times \frac { \partial s } { \partial \theta } \| d \theta d \phi \)