7. Find each limit or show that the limit does not exist: 2x²y² - 2 lim (x,y) →(1,1) x² + y² -2° (a) (b) (c) xy+1 lim (x,y) →(0,0) x² + y² +1° x² + y² lim (x,y) →(0,0) √√x² + y² + 1 − 1°
7. Find each limit or show that the limit does not exist: 2x²y² - 2 lim (x,y) →(1,1) x² + y² -2° (a) (b) (c) xy+1 lim (x,y) →(0,0) x² + y² +1° x² + y² lim (x,y) →(0,0) √√x² + y² + 1 − 1°
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
Calculus
![**Exercise 7: Find each limit or show that the limit does not exist:**
(a)
\[
\lim_{(x,y) \to (1,1)} \frac{2x^2y^2 - 2}{x^2 + y^2 - 2}.
\]
(b)
\[
\lim_{(x,y) \to (0,0)} \frac{xy + 1}{x^2 + y^2 + 1}.
\]
(c)
\[
\lim_{(x,y) \to (0,0)} \frac{x^2 + y^2}{\sqrt{x^2 + y^2 + 1} - 1}.
\]
**Exercise 8:** If
\[
\lim_{(x,y) \to (3,8)} f(x,y) = 2022,
\]
what can you say about the value of \( f(13,8) \)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1784d6b6-d0da-4ca6-88bb-f1a2aff3fb92%2Fb8ec900a-521b-4190-8f98-66a2657a4423%2Fwl6thio_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise 7: Find each limit or show that the limit does not exist:**
(a)
\[
\lim_{(x,y) \to (1,1)} \frac{2x^2y^2 - 2}{x^2 + y^2 - 2}.
\]
(b)
\[
\lim_{(x,y) \to (0,0)} \frac{xy + 1}{x^2 + y^2 + 1}.
\]
(c)
\[
\lim_{(x,y) \to (0,0)} \frac{x^2 + y^2}{\sqrt{x^2 + y^2 + 1} - 1}.
\]
**Exercise 8:** If
\[
\lim_{(x,y) \to (3,8)} f(x,y) = 2022,
\]
what can you say about the value of \( f(13,8) \)?
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