Check all the statements about an arbitrary function f(x, y) and an arbitrary point (a, b) that are true:afafanddydifferentiable at (a, b).O Ifexist in a neighborhod of (a, b) and are continuous at (a, b) then f(z, y) isafafandalways exist.dylim(1,9) → (a,b)f(z, y) always exists.O If f(x, y) is differentiable at (a, b) then a tangent plane to f(r, y) exists at (a, b).O If f(z, y) is continuous at (a, b) then it is differentiable at (a, b).O If f(x, y) is differentiable at (a, b) then it is continuous at (a, b).O f(1, y) must have a tangent plane at (a, b).

This is a problem of multivariable calculus.

O If and exist in a neighborhod of (a, b) and are continuous at (a, b) then f(x, y) is differentiable at (a, b). af af and always exist. dy lim (1,9) → (a, b) O f f(x, y) is differentiable at (a, b) then a tangent plane to f(x, y) exists at (a, b). O if f(z, y) is continuous at (a, b) then it is differentiable at (a, b). O if f(z, y) is differentiable at (a, b) then it is continuous at (a, b). f(x, y) always exists.

O If and exist in a neighborhod of (a, b) and are continuous at (a, b) then f(x, y) is differentiable at (a, b). af af and always exist. dy lim (1,9) → (a, b) O f f(x, y) is differentiable at (a, b) then a tangent plane to f(x, y) exists at (a, b). O if f(z, y) is continuous at (a, b) then it is differentiable at (a, b). O if f(z, y) is differentiable at (a, b) then it is continuous at (a, b). f(x, y) always exists.

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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