Chapter 1: Problem 14
Find the slope and the \(y\) -intercept (if possible) of the line. $$ y=-1 $$
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Write the expression in algebraic form. \(\sin (\arccos x)\)
In Exercises \(25-34,\) find the limit. $$ \lim _{x \rightarrow 1 / 2} x^{2} \tan \pi x $$
Writing Use a graphing utility to graph \(f(x)=x, \quad g(x)=\sin x, \quad\) and \(\quad h(x)=\frac{\sin x}{x}\) in the same viewing window. Compare the magnitudes of \(f(x)\) and \(g(x)\) when \(x\) is "close to" \(0 .\) Use the comparison to write \(a\) short paragraph explaining why \(\lim _{x \rightarrow 0} h(x)=1\).
Use a graphing utility to graph the function on the interval \([-4,4] .\) Does the graph of the function appear continuous on this interval? Is the function continuous on [-4,4]\(?\) Write a short paragraph about the importance of examining a function analytically as well as graphically. $$ f(x)=\frac{e^{-x}+1}{e^{x}-1} $$
Average Speed On a trip of \(d\) miles to another city, a truck driver's average speed was \(x\) miles per hour. On the return trip. the average speed was \(y\) miles per hour. The average speed for the round trip was 50 miles per hour. (a) Verify that \(y=\frac{25 x}{x-25}\) What is the domain? (b) Complete the table. \begin{tabular}{|l|l|l|l|l|} \hline\(x\) & 30 & 40 & 50 & 60 \\ \hline\(y\) & & & & \\ \hline \end{tabular} Are the values of \(y\) different than you expected? Explain. (c) Find the limit of \(y\) as \(x \rightarrow 25^{+}\) and interpret its meaning.
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