Please Help! Use the two-path test to prove that the following limit does not exist.y-2x²lim4(ху) — (0,0) у" +х*.....y-2x2What 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-2x2What value does f(x,y)=Dapproach 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. 2y +xO 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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Answered: Use the two-path test to prove that the…

Math

Calculus

Use the two-path test to prove that the following limit does not exist. y-2x2 lim y+x (x.y)-(0,0)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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Question

Please Help!

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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