(a) (b) 2x²y x + y² x² + 6xy+8y² lim (x,y) →(1,1) 2x² +5y² - x lim (x,y)→(3,2)
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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Question
find the limit for the following expression
![The image contains two mathematical expressions which are limits involving functions of two variables, \(x\) and \(y\).
### (a)
The limit is expressed as:
\[
\lim_{(x, y) \to (3, 2)} \frac{2x^2y}{x + y^2}
\]
### (b)
The limit is expressed as:
\[
\lim_{(x, y) \to (1, 1)} \frac{x^2 + 6xy + 8y^2}{2x^2 + 5y^2 - x}
\]
These expressions involve evaluating limits as the variables \(x\) and \(y\) approach specific points: (3, 2) and (1, 1), respectively. Each limit calculation requires determining the behavior of a given rational function as \(x\) and \(y\) approach these points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1079eff7-cd9f-4a9b-a6b7-8587fcd056cc%2F57ccdf76-ddd3-400f-915a-1c52545b0cb6%2Fym3exm3_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains two mathematical expressions which are limits involving functions of two variables, \(x\) and \(y\).
### (a)
The limit is expressed as:
\[
\lim_{(x, y) \to (3, 2)} \frac{2x^2y}{x + y^2}
\]
### (b)
The limit is expressed as:
\[
\lim_{(x, y) \to (1, 1)} \frac{x^2 + 6xy + 8y^2}{2x^2 + 5y^2 - x}
\]
These expressions involve evaluating limits as the variables \(x\) and \(y\) approach specific points: (3, 2) and (1, 1), respectively. Each limit calculation requires determining the behavior of a given rational function as \(x\) and \(y\) approach these points.
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