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Chapter 12: Q. 3 (page 989)

Sketch the level curves f(x, y) = c of the following functions for c = 鈭�3, 鈭�2, 鈭�1, 0, 1, 2, and 3:

f(x,y)=x鈭�sin鈭�1鈦�y

Short Answer

Expert verified

Ans: The sketch is,

Step by step solution

01

Step 1. Given information.

given,

f(x,y)=x鈭�sin鈭�1鈦�y

02

Step 2.  Given surface is f(x,y)=x−sin−1⁡y to sketch the level curves take f(x,y)=c, so that  y=sin(x-c)

Then for c=鈭�3,y=sin鈦�(x+3)

Which is the equation of trigonometric sine function with origin shifted to left by 3

For c=鈭�2,y=sin鈦�(x+2)

Which is the equation of trigonometric sine function with origin shifted to left by 2
For c=鈭�1,y=sin鈦�(x+1)

Which is the equation of trigonometric sine function with origin shifted to left by 1

03

Step 3. Now,

For c=0,y=sin鈦�x

Which is the equation of trigonometric sine function.

For c=1,y=sin鈦�(x鈭�1)

Which is the equation of trigonometric sine function with origin shifted to the right by 1
For c=2,y=sin鈦�(x鈭�2)

Which is the equation of trigonometric sine function with origin shifted to the right by 2

For c=3,y=sin鈦�(x鈭�3)

Which is the equation of trigonometry sin function with origin shifted o right by 3

04

Step 4. These curves are sketched below

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Most popular questions from this chapter

Partial derivatives: Find all first- and second-order partial derivatives for the following functions:

f(x,y)=tan鈭�1yx

In Exercises 21鈥�26, find the discriminant of the given function.

gx,y=e-3xsin2y.

Achainruleforfunctionsoftwovariables:Letf(x,y)=x2y3,x=scost,andy=ssint.Find鈭�f鈭�xand鈭�f鈭�y.

Describe the meanings of each of the following mathematical expressions:

鈭�f(x,y)

Evaluate the following limits, or explain why the limit does not exist.

lim(x,y)鈫�(1,2)x2+y2x2-y2
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