Chapter 9: Problem 26
The revenue \(R\) for a company selling \(x\) units is \(R=900 x-0.1 x^{2}\) Use differentials to approximate the change in revenue if sales increase from \(x=3000\) to \(x=3100\) units.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Compare the values of \(d y\) and \(\Delta y\). \(y=0.5 x^{3} \quad x=2 \quad \Delta x=d x=0.1\)
Marginal Analysis, use differentials to approximate the change in cost, revenue, or profit corresponding to an increase in sales of one unit. For instance, in Exercise 29, approximate the change in cost as \(x\) increases from 12 units to 13 units. Then use a graphing utility to graph the function, and use the trace feature to verify your result. \(C=0.025 x^{2}+8 x+5 \quad x=10\)
Compare the values of \(d y\) and \(\Delta y\). \(y=x^{4}+1 \quad x=-1 \quad \Delta x=d x=0.01\)
Let \(x=2\) and complete the table for the function. $$ \begin{array}{|c|c|c|c|c|} \hline d x=\Delta x & d y & \Delta y & \Delta y-d y & d y / \Delta y \\ \hline 1.000 & & & & \\ \hline 0.500 & & & & \\ \hline 0.100 & & & & \\ \hline 0.010 & & & & \\ \hline 0.001 & & & & \\ \hline \end{array} $$ \(y=\frac{1}{x^{2}}\)
Use a graphing utility to graph the function. Explain why there is no vertical asymptote when a superficial examination of the function may indicate that there should be one. \(g(x)=\frac{x^{2}+x-2}{x-1}\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
