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5. Show that the following functions ry (x² - y²) x² + y² (a) f(x, y) = 0, (b) f(x, y) = if (x² + y²) 0 if (x² + y²) = 0 have first order partial derivatives at (0,0), and discuss the differentiability at (0,0). if (x² + y²) #0 if (r² + y²) = 0 r² + y²

5. Show that the following functions ry (x² - y²) x² + y² (a) f(x, y) = 0, (b) f(x, y) = if (x² + y²) 0 if (x² + y²) = 0 have first order partial derivatives at (0,0), and discuss the differentiability at (0,0). if (x² + y²) #0 if (r² + y²) = 0 r² + y²

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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5. Show that the following functions ry (r-y) + y? lo if (r + y) # 0 (a) f(r, y)= if (r+y) = 0 if (z2 + y) 0 (b) f(r, y) = r2+ y2 0, if (2 + y) = 0 have first order partial derivatives at (0, 0), and discuss the differentiability at (0,0). 6. Show that following function
Transcribed Image Text:5. Show that the following functions ry (r-y) + y? lo if (r + y) # 0 (a) f(r, y)= if (r+y) = 0 if (z2 + y) 0 (b) f(r, y) = r2+ y2 0, if (2 + y) = 0 have first order partial derivatives at (0, 0), and discuss the differentiability at (0,0). 6. Show that following function
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