Current Attempt in Progress With \( t \) in years since 2016, the height of a sand dune (in centimeters) is \( f(t)=550-2 t^{2} \). Find \( f(5) \) and \( f^{\prime}(5) \). Using units, explain what each means in terms of the sand dune. \( f(5)= \) \( f^{\prime}(5)= \) In the year i eTextbook and Media

12) \( \frac{\sqrt{x+2}-\sqrt{x-2}}{\sqrt{x+2}+\sqrt{x-2}}=\frac{x}{2} \)

1. Resole \( y=\frac{x^{3}+5 x^{2}-6 x+6}{(x-1)^{2}\left(x^{2}+2\right)} \) in to partial \( = \) fraction: Hence find \( \int y d x \) and \( \frac{d y}{d x} \quad(12 \) math \( ) \) \[ (x-1)^{2} \]

If a function \( f \) is increasing on the intervals \( [-3,1] \) and \( [9,19] \) and decreasing on the interval \( [1,9] \), determine the interval(s) on which \( g(x)=-2 f(2 x-7) \) is increasing. The graph \( g(x)=-2 f(2 x-7) \) is increasing on interval \( (4,8) \). \[ \begin{array}{l}\text { (Type your answer in interval notation.) }\end{array} \]

Let \( y=5 x^{2}+2 x+3 \). If \( \Delta x=0.2 \) at \( x=4 \), use linear approximation to estimate \( \Delta y \) \( \Delta y \approx \)

Verify that the equation is an identity. \[ \frac{\csc x}{\cot x}=\sec x \]