answer only e and f Consider the function f whose graph is shown below.This function is given by=f(0,0)=lim f(x, 0) =x-0=f(x, y) ={Z3ryx² + y²0,(a) Find a formula for the single variable function f(0, y).f(0, y) =What is f(0, 0) for this function?f(0,0) =Find its limit as y → 0:lim f(0, y)y+0f(x, mx) =X(b) Based on your work in (a), is the single variable function f(0, y) continuous? ? ✪(c) Next, similarly consider f(x, 0).f(x, 0) =(x, y) = (0,0)(x, y) = (0,0).(d) Based on this work in (a), is the single variable function f(x, 0) continuous? ? ✪(e) Finally, consider f along rays emanating from the origin. Note that these are given byy = mx, for some (constant) value of m.Find and simplify fon the ray y = x:f(x, x) =(Notice that this means that y = x is a contour of f. Be sure you can explain why this is.)Find and simplify f on any ray y = mx.[(Again, notice that this means that any ray y = mx is a contour of f; be sure you canexplain why.)(f) is f(x, y) continuous at (0, 0)? ? ✪

Answered: Image /qna-images/answer/c14f0eb0-e7c2-4c7d-b128-dd746d1038b6.jpg

(e) Finally, consider f along rays emanating from the origin. Note that these are given by y = mx, for some (constant) value of m. Find and simplify f on the ray y = x: f(x, x) = (Notice that this means that y = x is a contour of f. Be sure you can explain why this is.) Find and simplify fon any ray y = mx. f(x, mx) = (Again, notice that this means that any ray y = mx is a contour of f; be sure you can explain why.) (f) is f(x, y) continuous at (0,0)? ? ✪

(e) Finally, consider f along rays emanating from the origin. Note that these are given by y = mx, for some (constant) value of m. Find and simplify f on the ray y = x: f(x, x) = (Notice that this means that y = x is a contour of f. Be sure you can explain why this is.) Find and simplify fon any ray y = mx. f(x, mx) = (Again, notice that this means that any ray y = mx is a contour of f; be sure you can explain why.) (f) is f(x, y) continuous at (0,0)? ? ✪

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 15T

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