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Chapter 12: Q. 1 (page 988)

Level curves: Sketch the level curves $f (x, y) = c$ of the following functions for $c = - 3, - 2, - 1, 0, 1, 2, 3$
$f (x, y) = - \frac{2 y}{x}$

Short Answer

Expert verified

The level curve is shown in the figure

Step by step solution

01

Step 1. Given Information

The given function $f (x, y) = - \frac{2 y}{x}$ and $c = - 3, - 2, - 1, 0, 1, 2, 3$

For each value of $c,$ we will graph the set of points that are solutions of the equation $- \frac{y}{2 x} = c$ .

02

Step 2. For c=0

$f (x, y) = c - \frac{2 y}{x} = 0 g i v e s y = 0$

Thus, level curve here is $x$ axis.

03

Step 3. For c=1

$f (x, y) = c - \frac{2 y}{x} = 1 x = - 2 y y = - \frac{1}{2} x$

At this point, we recognize that level curve when $c = 1$ is a straight line

04

Step 4. For next values

05

Step 5. Level Curves

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