Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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![Use the two-path test to prove that the following limit does not exist.
y-2x²
lim
4
(ху) — (0,0) у" +х*
.....
y-2x2
What value does f(x,y) =
approach as (x,y) approaches (0,0) along the x-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
+X+
O A. f(x,y) approaches
(Simplify your answer.)
O B. f(x,y) approaches - o.
O C. f(x,y) approaches o.
O D. f(x,y) has no limit as (x,y) approaches (0,0) along the x-axis.
y-2x2
What value does f(x,y)=D
approach as (x y) approaches (0,0) along the y-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
.4. 2
y +x
O A. f(x,y) approaches
(Simplify your answer)
O B. f(x,y) approaches co.
O C. f(x,y) approaches - o.
O D. f(x,y) has no limit as (x,y) approaches (0,0) along the y-axis.
Why does the given limit not exist?
O A. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value.
O B. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values.
O C. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81b1cfc8-e08e-449c-bbfd-a1976918605a%2F969ea7cd-5d30-4597-a636-f2440be24875%2F5ij3yas_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use the two-path test to prove that the following limit does not exist.
y-2x²
lim
4
(ху) — (0,0) у" +х*
.....
y-2x2
What value does f(x,y) =
approach as (x,y) approaches (0,0) along the x-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
+X+
O A. f(x,y) approaches
(Simplify your answer.)
O B. f(x,y) approaches - o.
O C. f(x,y) approaches o.
O D. f(x,y) has no limit as (x,y) approaches (0,0) along the x-axis.
y-2x2
What value does f(x,y)=D
approach as (x y) approaches (0,0) along the y-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
.4. 2
y +x
O A. f(x,y) approaches
(Simplify your answer)
O B. f(x,y) approaches co.
O C. f(x,y) approaches - o.
O D. f(x,y) has no limit as (x,y) approaches (0,0) along the y-axis.
Why does the given limit not exist?
O A. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value.
O B. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values.
O C. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value.
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