Chapter 11: Problem 61
Define a function of two variables.
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
Find a normal vector to the level curve \(f(x, y)=c\) at \(P.\) $$ \begin{array}{l} f(x, y)=\frac{x}{x^{2}+y^{2}} \\ c=\frac{1}{2}, \quad P(1,1) \end{array} $$
Area Let \(\theta\) be the angle between equal sides of an isosceles triangle and let \(x\) be the length of these sides. \(x\) is increasing at \(\frac{1}{2}\) meter per hour and \(\theta\) is increasing at \(\pi / 90\) radian per hour. Find the rate of increase of the area when \(x=6\) and \(\theta=\pi / 4\).
Describe the difference between the explicit form of a function of two variables \(x\) and \(y\) and the implicit form. Give an example of each.
Describe the change in accuracy of \(d z\) as an approximation of \(\Delta z\) as \(\Delta x\) and \(\Delta y\) increase.
In Exercises \(43-46,\) find \(\partial w / \partial s\) and \(\partial w / \partial t\) by using the appropriate Chain Rule. \(w=x y z, \quad x=s+t, \quad y=s-t, \quad z=s t^{2}\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
