Chapter 0: Problem 7
Find \(a\) if the line passing through \((1,3)\) and \((-4, a)\) has slope 5.
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Plot the graph of the function \(f\) in an appropriate viewing window. (Note: The answer is not unique.) $$ \begin{array}{l} f(x)=-2 x^{4}+5 x^{2}-4\\\ \text { 7. } f(x)=\frac{x^{3}}{x^{3}+1} \end{array} $$
Find the exact value of the given expression. $$ \sin ^{-1} 0 $$
Show that \(f\) and \(g\) are inverses of each other by verifying that \(f[g(x)]=x\) and \(g[f(x)]=x\). $$ f(x)=\frac{1}{x} ; \quad g(x)=\frac{1}{x} $$
Plot the graph of the function \(f\) in an appropriate viewing window. (Note: The answer is not unique.) $$ f(x)=2 x^{4}-3 x^{3}+5 x^{2}-20 x+40 $$
Let \(f(x)=\left(1+\frac{1}{x}\right)^{x}\), where \(x>0\). a. Plot the graph of \(f\) using the window \([0,10] \times[0,3]\), and then using the window \([0,100] \times[0,3] .\) Does \(f(x)\) appear to approach a unique number as \(x\) gets larger and larger? b. Use the evaluation function of your graphing utility to fill in the accompanying table. Use the table of values to estimate, accurate to five decimal places, the number that \(f(x)\) seems to approach as \(x\) increases without bound. Note: We will see in Section \(2.8\) that this number, written \(e\), is given by \(2.71828 \ldots\)
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