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Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by drawing an assortment of level curves in the function's domain. f(x,y) = y2 a. Choose the correct sketch of f(x,y) = y2 below. O A. OC. b. Choose the correct graph of the level curves below. OA. OB. Oc. Ay Ay

Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by drawing an assortment of level curves in the function's domain. f(x,y) = y2 a. Choose the correct sketch of f(x,y) = y2 below. O A. OC. b. Choose the correct graph of the level curves below. OA. OB. Oc. Ay Ay

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 44E
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Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by drawing an assortment of level curves in the function's domain. f(x,y) = y2 a. Choose the correct sketch of f(x,y) = y? below. A. В. С. y b. Choose the correct graph of the level curves below. O A. В. C. Ay
Transcribed Image Text:Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by drawing an assortment of level curves in the function's domain. f(x,y) = y2 a. Choose the correct sketch of f(x,y) = y? below. A. В. С. y b. Choose the correct graph of the level curves below. O A. В. C. Ay
By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0). f(x,y) = 4 x' + Examine the values of f along curves that end at (0,0). Along which set of curves is fa constant value? A. y= kx, x# 0 B. y= kx?, x+0 Oc. y= kx + kx², x#0 O D. y= kx³, x# 0 If (x,y) approaches (0,0) along the curve when k=1 used in the set of curves found above, what is the limit? (Simplify your answer.) If (x,y) approaches (0,0) along the curve when k= 0 used in the set of curves found above, what is the limit? (Simplify your answer.) What can you conclude? O A. Since f has two different limits along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0). B. Since f has the same limit along two different paths to (0,0), by the two-path test, f has no limit as (x,y) approaches (0,0). C. Since f has two different limits along two different paths to (0,0), by the two-path test, f has no limit as (x,y) approaches (0,0). D. Since f has the same limit along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0).
Transcribed Image Text:By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0). f(x,y) = 4 x' + Examine the values of f along curves that end at (0,0). Along which set of curves is fa constant value? A. y= kx, x# 0 B. y= kx?, x+0 Oc. y= kx + kx², x#0 O D. y= kx³, x# 0 If (x,y) approaches (0,0) along the curve when k=1 used in the set of curves found above, what is the limit? (Simplify your answer.) If (x,y) approaches (0,0) along the curve when k= 0 used in the set of curves found above, what is the limit? (Simplify your answer.) What can you conclude? O A. Since f has two different limits along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0). B. Since f has the same limit along two different paths to (0,0), by the two-path test, f has no limit as (x,y) approaches (0,0). C. Since f has two different limits along two different paths to (0,0), by the two-path test, f has no limit as (x,y) approaches (0,0). D. Since f has the same limit along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0).
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