Explain why the following justification is incorrect:To evaluate the limit of the functionx² + y²lim(x,y) →(0,0) 1+ y² ¹we can approach the point (0,0) along different paths and see if the limit is the same regardless ofthe path taken.First, let's consider the path along the x-axis ($y = 0$). We have:x² + 0²lim(x,0) (0,0) 1+0²x²lim(x,0) (0,0) 1Next, let's consider the path along the y-axis ($x = 0$). We have:0² + y²lim(0,y) →(0,0) 1+ y²=y²lim(0,y) →(0,0) 1+ y²= 0.-0.Since the limit is O along both paths, we can conclude that the limit of the given function as (x, y)approaches (0, 0) is 0.Enter your answer here

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Explain why the following justification is incorrect: To evaluate the limit of the function x² + y² 2 lim (x,y) →(0,0) 1+ y² we can approach the point (0,0) along different paths and see if the limit is the same regardless of the path taken. First, let's consider the path along the x-axis ($y = 0$). We have: x² + 0² lim (,0) (0,0) 1+0² lim (x,0) (0,0) 1 Next, let's consider the path along the y-axis ($x = 0$). We have: 0² + y² lim (0,y) →(0,0) 1+ y² = 0. y² lim (0,y) (0,0) 1+ y² = 0. Since the limit is 0 along both paths, we can conclude that the limit of the given function as (x, y) approaches (0, 0) is 0. Enter your answer here

Explain why the following justification is incorrect: To evaluate the limit of the function x² + y² 2 lim (x,y) →(0,0) 1+ y² we can approach the point (0,0) along different paths and see if the limit is the same regardless of the path taken. First, let's consider the path along the x-axis ($y = 0$). We have: x² + 0² lim (,0) (0,0) 1+0² lim (x,0) (0,0) 1 Next, let's consider the path along the y-axis ($x = 0$). We have: 0² + y² lim (0,y) →(0,0) 1+ y² = 0. y² lim (0,y) (0,0) 1+ y² = 0. Since the limit is 0 along both paths, we can conclude that the limit of the given function as (x, y) approaches (0, 0) is 0. Enter your answer here

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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