Briefly explain why following are true or false. The answer must include an expl

Question

Briefly explain why following are true or false. The answer must include an explanation, the explanation must provide the rationale for the true-false answer.

1. The existence of all a functions partial dervivatives at a point confirm that the function is continuous there

2. If two nonzero directional derivatives at a point have the same value, their gradients are equal

3. If the directional derivative of f(x,y) exists, Du f(x,y) is not equal to Dv f(x,y) where unit vectors u = - v

4. To have an extremum at a point in N dimensional space, the N partial dervivatives must exist and must equal zero there

5. If the limit of f(2,y) = 6 as y approaches 3, then the limit of f(x,y) = 6 as (x,y) approaches (2,3)

Explanation / Answer

true,true,false,true,false

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