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e. In general, if lim(z,y)→(0,0) J approaches (0, 0), regardless of the path we take in letting (x, y) → (0,0). Explain what the last two parts of this activity imply about the existence of lim (z,y)+(0,0) f(x,y).

e. In general, if lim(z,y)→(0,0) J approaches (0, 0), regardless of the path we take in letting (x, y) → (0,0). Explain what the last two parts of this activity imply about the existence of lim (z,y)+(0,0) f(x,y).

Advanced Engineering Mathematics
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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Consider the function g(x,y) = x2y/x4+y2 and investigate the limit lim(x,y)→(0,0) g(x,y)

I need help with e. I have attached photos of the previous 2 problems the question is referencing 

CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS d. What is the behavior of f along the line y = when z> 0; that is, what is the value of f(x,x) when z> 0? If we approach (0,0) by moving along the line y = x in the first quadrant (thus considering ƒ(x,x) limit? Along the as x → 0+, what value do we as live, f (x,y) reduces find the to f(x,x) f(x,x) ==> == (x 52 √x²+x² √2x² va xa (x,x)=√ y = x; X 70 -X x√2 iMECKY limf(x, xL lim y for x → OT -X²20+ (₂) a longline y=x - e. In general, if fim(z,y)→(0,0) f (x, y) = L, then f (x, y) approaches Las (x,y) X0 as 20 approaches (0, 0), regardless of the path we take in letting (x,y) → (0,0). Explain what the last two parts of this activity imply about the existence of lim(x,y)→(0,0) f(x, y). C
Transcribed Image Text:CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS d. What is the behavior of f along the line y = when z> 0; that is, what is the value of f(x,x) when z> 0? If we approach (0,0) by moving along the line y = x in the first quadrant (thus considering ƒ(x,x) limit? Along the as x → 0+, what value do we as live, f (x,y) reduces find the to f(x,x) f(x,x) ==> == (x 52 √x²+x² √2x² va xa (x,x)=√ y = x; X 70 -X x√2 iMECKY limf(x, xL lim y for x → OT -X²20+ (₂) a longline y=x - e. In general, if fim(z,y)→(0,0) f (x, y) = L, then f (x, y) approaches Las (x,y) X0 as 20 approaches (0, 0), regardless of the path we take in letting (x,y) → (0,0). Explain what the last two parts of this activity imply about the existence of lim(x,y)→(0,0) f(x, y). C
f. State whether the limit lim(z,y) →(0,0) g(x, y) exists or not and provide a justification of your statement. Since we do not have the same limit vale a long the curve, the limit doesn't exist.
Transcribed Image Text:f. State whether the limit lim(z,y) →(0,0) g(x, y) exists or not and provide a justification of your statement. Since we do not have the same limit vale a long the curve, the limit doesn't exist.
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