91Ó°ÊÓ

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

Right-triangle relationships Draw a right triangle to simplify the given expressions. Assume \(x>0.\) $$\sin \left(\cos ^{-1}(x / 2)\right)$$

Find a simple function that fits the data in the tables. $$\begin{array}{|r|r|} \hline x & y \\ \hline 0 & -1 \\ \hline 1 & 0 \\ \hline 4 & 1 \\ \hline 9 & 2 \\ \hline 16 & 3 \\ \hline \end{array}$$

Find a formula for a function describing the given situation. Graph the function and give a domain that makes sense for the problem. Recall that with constant speed, distance \(=\)speed time elapsed.A function \(y=f(x)\) such that \(y\) is 1 less than the cube of \(x\).

Right-triangle relationships Draw a right triangle to simplify the given expressions. Assume \(x>0.\) $$\sin ^{-1}(\cos \theta), \text { for } 0 \leq \theta \leq \pi / 2$$

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. $$\log _{3} 30$$

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

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

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

Simplify the difference quotient\(\frac{f(x)-f(a)}{x-a}\) for the following functions. $$f(x)=x^{4}$$