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Given if (x,y) (0,0) f(x, y) = x4+ y6 %3D if (x, y) = (0,0) where a and b are nonnegative integers. For each part, determine whether f(x, y) satisfies the given condition for the specified values of a and b. Part A. For a = 4 and b = 1: f(x,y) is continuous at (0, 0). Part B. For a = 3 and b = 1: f(r, y) goes to 1 as (x, y) approaches (0, 0) along the y = x, and f(T, y) goes to -1 as (x, y) approaches (0,0) along the line y = -x. %3D

Given if (x,y) (0,0) f(x, y) = x4+ y6 %3D if (x, y) = (0,0) where a and b are nonnegative integers. For each part, determine whether f(x, y) satisfies the given condition for the specified values of a and b. Part A. For a = 4 and b = 1: f(x,y) is continuous at (0, 0). Part B. For a = 3 and b = 1: f(r, y) goes to 1 as (x, y) approaches (0, 0) along the y = x, and f(T, y) goes to -1 as (x, y) approaches (0,0) along the line y = -x. %3D

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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Given if (x,y) + (0,0) f(x, y) = x4 + y° 0. if (r, y) = (0,0) where a and b are nonnegative integers. For each part, determine whether f(r, y) satisfies the given condition for the specified values of a and b. Part A. For a = 4 and b = 1: f(x, y) is continuous at (0, 0). Part B. For a = 3 and b = 1: f(x, y) goes to 1 as (x, y) approaches (0,0) along the y = x, and f(T, y) goes to –1 as (x, y) approaches (0, 0) along the line y = -x. Part C. For a = 1 and b = 1: f(x, y) is not differentiable at (1, 1).
Transcribed Image Text:Given if (x,y) + (0,0) f(x, y) = x4 + y° 0. if (r, y) = (0,0) where a and b are nonnegative integers. For each part, determine whether f(r, y) satisfies the given condition for the specified values of a and b. Part A. For a = 4 and b = 1: f(x, y) is continuous at (0, 0). Part B. For a = 3 and b = 1: f(x, y) goes to 1 as (x, y) approaches (0,0) along the y = x, and f(T, y) goes to –1 as (x, y) approaches (0, 0) along the line y = -x. Part C. For a = 1 and b = 1: f(x, y) is not differentiable at (1, 1).
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