91Ó°ÊÓ

Find the following points of intersection. The point(s) of intersection of the curves \(y=4 \sqrt{2 x}\) and \(y=2 x^{2}\).

Simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the following functions. $$f(x)=x^{2}$$

The height in feet of a baseball hit straight up from the ground with an initial velocity of \(64 \mathrm{ft} / \mathrm{s}\) is given by \(h=f(t)=64 t-16 t^{2},\) where \(t\) is measured in seconds after the hit. a. Is this function one-to-one on the interval \(0 \leq t \leq 4 ?\) b. Find the inverse function that gives the time \(t\) at which the ball is at height \(h\) as the ball travels upward. Express your answer in the form \(t=f^{-1}(h)\) c. Find the inverse function that gives the time \(t\) at which the ball is at height \(h\) as the ball travels downward. Express your answer in the form \(t=f^{-1}(h)\) d. At what time is the ball at a height of 30 ft on the way up? e. At what time is the ball at a height of \(10 \mathrm{ft}\) on the way down?

Draw a right triangle to simplify the given expressions. Assume \(x>0\) $$\cos \left(2 \sin ^{-1} x\right)\left(\text {Hint}: \text { Use } \cos 2 \theta=\cos ^{2} \theta-\sin ^{2} \theta .\right)$$

Simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the following functions. $$f(x)=2 x^{2}-3 x+1$$

Find the following points of intersection. The point(s) of intersection of the parabola \(y=x^{2}+2\) and the line \(y=x+4\)

Prove the following identities. $$\sec \theta=\frac{1}{\cos \theta}$$

Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places. $$\log _{2} 15$$

Find the following points of intersection. The point(s) of intersection of the parabolas \(y=x^{2}\) and \(y=-x^{2}+8 x\)

Simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the following functions. $$f(x)=\frac{2}{x}$$