Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
2ху lim (x.y)-(1.0) Which one of the following statements is correct? (a) Consider the limit OThe limit does not exist. OThe limit is infinite. OThe limit exists and is equal to 0). OThe limit exists and is equal to 1. ONone of the previous statements is correct. (b) Consider the limit lim (x)-(0.0) x2 Suppose that you want to test the limit along all lines passing through (0, 0). Which one of the following statements is correct? +y OOne obtains the same limit along all lines, so the limit must exist. OOne obtains the same limit along all lines, but the limit might not exist. OOne obtains two different limits along two different lines, so the limit does not exist. OOne obtains two different limits along two different lines, but the limit might still exist. ONone of the previous statements is correct. (c) Consider the function defined by y f(x, y) = - for (x, y) # (0, 0) and f(0, 0) = +. Which one of the following statements is correct? OThe function is continuous at all points. OThe function is continuous at all points except for (0, 0). OThe function is continuous at all points except for those of the form (x, x) for x € R. OThe function is continuous at all points except for those of the form (x, x) for x €R \ {1, –1}. OThe function is never continuous, because it is not well-defined. ONone of the previous statements is correct. (d) Consider the function n f(x, y) = |x| - y3. Which one of the following statements is correct? OThe function is differentiable at (0,0). OThe function is not differentiable at (0,0), because the partial derivative with respect to x does not exist. OThe function is not differentiable at (0,0), because the partial derivative with respect to y does not exist. OThe function is not differentiable, because the partial derivatives are not defined for some points near (0,0).

2ху lim (x.y)-(1.0) Which one of the following statements is correct? (a) Consider the limit OThe limit does not exist. OThe limit is infinite. OThe limit exists and is equal to 0). OThe limit exists and is equal to 1. ONone of the previous statements is correct. (b) Consider the limit lim (x)-(0.0) x2 Suppose that you want to test the limit along all lines passing through (0, 0). Which one of the following statements is correct? +y OOne obtains the same limit along all lines, so the limit must exist. OOne obtains the same limit along all lines, but the limit might not exist. OOne obtains two different limits along two different lines, so the limit does not exist. OOne obtains two different limits along two different lines, but the limit might still exist. ONone of the previous statements is correct. (c) Consider the function defined by y f(x, y) = - for (x, y) # (0, 0) and f(0, 0) = +. Which one of the following statements is correct? OThe function is continuous at all points. OThe function is continuous at all points except for (0, 0). OThe function is continuous at all points except for those of the form (x, x) for x € R. OThe function is continuous at all points except for those of the form (x, x) for x €R \ {1, –1}. OThe function is never continuous, because it is not well-defined. ONone of the previous statements is correct. (d) Consider the function n f(x, y) = |x| - y3. Which one of the following statements is correct? OThe function is differentiable at (0,0). OThe function is not differentiable at (0,0), because the partial derivative with respect to x does not exist. OThe function is not differentiable at (0,0), because the partial derivative with respect to y does not exist. OThe function is not differentiable, because the partial derivatives are not defined for some points near (0,0).

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

Need help with this question. Thank you :)

 

2ху lim (х,у)-(1,0) х2+ y? (a) Consider the limit Which one of the following statements is correct? OThe limit does not exist. OThe limit is infinite. OThe limit exists and is equal to (). OThe limit exists and is equal to 1. ONone of the previous statements is correct. (b) Consider the limit x + y² lim Suppose that you want to test the limit along all lines passing through (0, 0). Which one of the following statements is correct? (х,у)-(0,0) х2 +у OOne obtains the same limit along all lines, so the limit must exist. OOne obtains the same limit along all lines, but the limit might not exist. OOne obtains two different limits along two different lines, so the limit does not exist. OOne obtains two different limits along two different lines, but the limit might still exist. ONone of the previous statements is correct. (c) Consider the function defined by y f(x, y) = for (x, y) # (0, 0) and f(0, 0) = . x² + y? Which one of the following statements is correct? OThe function is continuous at all points. OThe function is continuous at all points except for (0, 0). OThe function is continuous at all points except for those of the form (x, x) for x E R. OThe function is continuous at all points except for those of the form (x, x) for x E R \ {1, –1}. OThe function is never continuous, because it is not well-defined. ONone of the previous statements is correct. (d) Consider the function n f(x, y) = |x| · y"3. Which one of the following statements is correct? OThe function is differentiable at (0,0). OThe function is not differentiable at (0,0), because the partial derivative with respect to x does not exist. OThe function is not differentiable at (0,0), because the partial derivative with respect to y does not exist. OThe function is not differentiable, because the partial derivatives are not defined for some points near (0,0). OThe function is not differentiable, because the partial derivatives are not continuous near (0,0). ONone of the previous statements is correct.
Transcribed Image Text:2ху lim (х,у)-(1,0) х2+ y? (a) Consider the limit Which one of the following statements is correct? OThe limit does not exist. OThe limit is infinite. OThe limit exists and is equal to (). OThe limit exists and is equal to 1. ONone of the previous statements is correct. (b) Consider the limit x + y² lim Suppose that you want to test the limit along all lines passing through (0, 0). Which one of the following statements is correct? (х,у)-(0,0) х2 +у OOne obtains the same limit along all lines, so the limit must exist. OOne obtains the same limit along all lines, but the limit might not exist. OOne obtains two different limits along two different lines, so the limit does not exist. OOne obtains two different limits along two different lines, but the limit might still exist. ONone of the previous statements is correct. (c) Consider the function defined by y f(x, y) = for (x, y) # (0, 0) and f(0, 0) = . x² + y? Which one of the following statements is correct? OThe function is continuous at all points. OThe function is continuous at all points except for (0, 0). OThe function is continuous at all points except for those of the form (x, x) for x E R. OThe function is continuous at all points except for those of the form (x, x) for x E R \ {1, –1}. OThe function is never continuous, because it is not well-defined. ONone of the previous statements is correct. (d) Consider the function n f(x, y) = |x| · y"3. Which one of the following statements is correct? OThe function is differentiable at (0,0). OThe function is not differentiable at (0,0), because the partial derivative with respect to x does not exist. OThe function is not differentiable at (0,0), because the partial derivative with respect to y does not exist. OThe function is not differentiable, because the partial derivatives are not defined for some points near (0,0). OThe function is not differentiable, because the partial derivatives are not continuous near (0,0). ONone of the previous statements is correct.
Expert Solution
Step 1

Each questions are solved with proper reasons.

steps

Step by step

Solved in 2 steps with 1 images

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