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Chapter 12: Q. 59 (page 917)

In Exercises 59鈥�62, match the given function of two variables with the surfaces in Figures I鈥揑V and with the level curves in Figures A鈥揇. Make sure you explain your reasoning

f(x,y)=x2-y2

Short Answer

Expert verified

The surface for the given function is figure A)

The level curve for the given function is figure A)

Step by step solution

01

Given information

We are given a functionf(x,y)=x2-y2

02

We match the level curves for the given function

We use 3D graphing utility to graph the given function

We get,

03

Find the level curve

The graph can be given as

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Most popular questions from this chapter

In Exercises 37-42, use the partial derivatives of role="math" localid="1650186824938" fx,y=xyand the point e,3specified to

afind the equation of the line tangent to the surface defined by the function in the xdirection,

bfind the equation of the line tangent to the surface defined by the function in the ydirection, and

cfind the equation of the plane containing the lines you found in parts aand b.

In Exercises 24鈥�32, find the maximum and minimum of the functionf subject to the given constraint. In each case explain why the maximum and minimum must both exist.

f(x,y,z)=xyzwhenx2+4y2+16z2=64

Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.

f(x,y)=xy鈥�P=(4,3)

Let f(x,y)be a differentiable function such that 鈭�f(x,y)鈮�0for every point in the domain of f, and let Rbe a closed, bounded subset of role="math" localid="1649887954022" 鈩�2.Explain why the maximum and minimum of f restricted to Roccur on the boundary ofrole="math" localid="1649888770915" R.

Solve the exact differential equations in Exercises 63鈥�66.ey+(xey鈭�7)dydx=0
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