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 FUNCTIONSd. What is the behavior of f along the line y = when z> 0; that is, whatis the value of f(x,x) when z> 0? If we approach (0,0) by moving alongthe line y = x in the first quadrant (thus considering ƒ(x,x)limit? Alongtheas x → 0+,what value do we as live, f (x,y) reducesfind theto f(x,x) f(x,x) ==>== (x52√x²+x² √2x²va xa(x,x)=√ y = x; X 70-Xx√2iMECKY limf(x, xL limy forx → 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 20approaches (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 existenceof 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 ajustification of your statement.Since we do not have the same limit valea long the curve, the limit doesn't exist.

Answer given below.As per your request I have solved part (e).

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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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