3940 A function f (x, y) is said to have a removable discontinuityat (x0, y0) if

Chapter 13, Problem 40

(choose chapter or problem)

A function \(f(x,y)\) is said to have a removable discontinuity at \(\left(x_{0}, y_{0}\right)\) if \(\lim _{(x, y) \rightarrow\left(x_{0}, y_{0}\right)} f(x, y)\) exists but \(f\) is not continuous at \(\left(x_{0}, y_{0}\right)\), either because \(f\) is not defined at \(\left(x_{0}, y_{0}\right)\) or because \(f\left(x_{0}, y_{0}\right)\) differs from the value of the limit. Determine whether \(f(x,y)\) has a removable discontinuity at \((0,0)\).

             \(f(x)=\left\{x^{2}+7 y^{2}, \quad \text { if }(x, y) \neq(0,0)-4, \quad i f(x, y)=(0,0)\right.\)

Equation Transcription:

 

Text Transcription:

f(x,y)

x_0,y_0

lim(x,y)→x_0,y_0  f(x,y)

f

fx_0,y_0

f(x,y)

(0,0)

f(x)={x^2+7y^2,  if (x,y) ≠ (0,0) -4,  if (x,y)=(0,0)