Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the function of two variables defined by f(x, y) = x³y² x6 + y² (a) Compute the limit of f(x, y) as (x,y) → (0,0) along the straight lines y = mx. (b) Now compute the limit of f(x, y) as (x, y) → (0,0) along the curves y = kx³/2 (c) Explain how the two-path test shows that this limit doesn't exist. As some final food for thought, consider how part (b) gave a definite numerical answer, and yet the limit does not exist. This is worth thinking about, even though there isn't an exercise here about that.

Consider the function of two variables defined by f(x, y) = x³y² x6 + y² (a) Compute the limit of f(x, y) as (x,y) → (0,0) along the straight lines y = mx. (b) Now compute the limit of f(x, y) as (x, y) → (0,0) along the curves y = kx³/2 (c) Explain how the two-path test shows that this limit doesn't exist. As some final food for thought, consider how part (b) gave a definite numerical answer, and yet the limit does not exist. This is worth thinking about, even though there isn't an exercise here about that.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Consider the function of two variables defined by f(x, y) = x³y² x6 + y² (a) Compute the limit of f(x, y) as (x,y) → (0,0) along the straight lines y = mx. (b) Now compute the limit of f(x, y) as (x, y) → (0,0) along the curves y = kx³/2 (c) Explain how the two-path test shows that this limit doesn't exist. As some final food for thought, consider how part (b) gave a definite numerical answer, and yet the limit does not exist. This is worth thinking about, even though there isn't an exercise here about that.
Transcribed Image Text:Consider the function of two variables defined by f(x, y) = x³y² x6 + y² (a) Compute the limit of f(x, y) as (x,y) → (0,0) along the straight lines y = mx. (b) Now compute the limit of f(x, y) as (x, y) → (0,0) along the curves y = kx³/2 (c) Explain how the two-path test shows that this limit doesn't exist. As some final food for thought, consider how part (b) gave a definite numerical answer, and yet the limit does not exist. This is worth thinking about, even though there isn't an exercise here about that.
Expert Solution
Step 1

The given function of two variables is f(x,y)=x3y2x6+y4.

(a) To Find: The limit of the function as (x,y)→(0,0) along the line y=mx.

(b) To Find: The limit of the function as (x,y)→(0,0) along the line y=kx3/2.

(c)To Explain: why the two path test above shows that limit does not exist when (x,y)→(0,0).

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS