(a, b), f (x, 42. Show that ifJ (2, Y) is differentiable at then the function of one variable J (2, 0) is differentiable at f (x, x = a. Use this to prove that I (, Y) = Vx" + Y“ is not differentiable at x² + y? (0,0).

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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42. Show that if \( f(x, y) \) is differentiable at \( (a, b) \), then the function of one variable \( f(x, b) \) is differentiable at \( x = a \). Use this to prove that \( f(x, y) = \sqrt{x^2 + y^2} \) is not differentiable at \( (0, 0) \).
Transcribed Image Text:**Further Insights and Challenges** 42. Show that if \( f(x, y) \) is differentiable at \( (a, b) \), then the function of one variable \( f(x, b) \) is differentiable at \( x = a \). Use this to prove that \( f(x, y) = \sqrt{x^2 + y^2} \) is not differentiable at \( (0, 0) \).
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