?For the following exercises, complete each task. Show that \(f(x, y)=x^{2}+3 y\) is
Chapter 4, Problem 193(choose chapter or problem)
For the following exercises, complete each task.
Show that \(f(x, y)=x^{2}+3 y\) is differentiable at every point. In other words, show that \(\Delta z=f(x+\Delta x, y+\Delta y)-f(x, y)=f_{x} \Delta x+f_{y} \Delta y+\varepsilon_{1} \Delta x+\varepsilon_{2} \Delta y\) where both \(\varepsilon_{1}\) and \(\varepsilon_{2}\) approach zero as \((\Delta x, \Delta y)\) approaches (0, 0).
Text Transcription:
f(x,y)=x^2+3 y
Delta_z=f(x+Delta.x,y+Delta.y)-f(x,y)=f_x_Delta.x+f_y_Delta.y+varepsilon_1_Delta.x+\varepsilon_2_Delta.y
varepsilon_1
varepsilon_2
Delta.x,Delta.y
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