Which one of the following functions below have no limit as (x, y) (0,0)? (Warning: Any wrong check will cancel a correct one!) x³ – y3 x² + y? f(x, y) xy cos(y) f(x, y) 3x2 + y² O f(x, y) = (x² + y³) In(æ² + y²) xyš x² + y6 f(x, y)

Which one of the following functions below have no limit as (x, y) (0,0)? (Warning: Any wrong check will cancel a correct one!) x³ – y3 x² + y? f(x, y) xy cos(y) f(x, y) 3x2 + y² O f(x, y) = (x² + y³) In(æ² + y²) xyš x² + y6 f(x, y)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as:

Question

Which one of the following functions below have no limit as (x, y) → (0,0)?
(Warning: Any wrong check will cancel a correct one!)
x³
f(x, y)
x² + y²
Ty cos(y)
3x2 + y²
f(x, y)
O f(x, y) = (x² + y²) In(x² + y²)
xy³
f(x, y)
x² + y6

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