GATE MA concept:directional-derivatives PYQs & Answers

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concept:directional-derivatives

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Questions 1–7 of 7. Imported answers require independent review unless marked reviewed.

Topic practice 7 questionsPage 1 of 1

Let

be a function defined as follows:

Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

is continuous at

For any

, the directional derivative of

in the direction of

exists.

is differentiable at

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Let

be a unit vector parallel to the tangent at the point

to the curve of intersection of the surfaces

and

. Then, the absolute value of the directional derivative of

in the direction of

is _____ (in integer)

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Let

be a function such that

Which of the following is/are correct?

Your answerSelect all correct options. You can choose more than one.

is continuous at

, but not differentiable at

is differentiable at

All the directional derivatives of

exist and they are equal to zero

Both the partial derivatives of

exist and they are equal to zero

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Let

be defined by

Then

Your answerSelect all correct options. You can choose more than one.

the directional derivative of

in the direction of

the directional derivative of

in the direction of

the directional derivative of

in the direction of

is NOT differentiable at

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Let

be given by

Consider the following statements: P:

is continuous at

but

is NOT differentiable at

. Q: The directional derivative

exists in the direction of every unit vector

. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

for

. Then the directional derivative of

in the direction

at the point

is ________.

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Let

be defined by

Then, at

Your answerChoose one option.

is continuous and the directional derivative of

does NOT exist in some direction

is NOT continuous and the directional derivatives of

exist in all directions

is NOT differentiable and the directional derivatives of

exist in all directions

is differentiable

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GATE MA concept:directional-derivatives PYQs

How to practice concept:directional-derivatives

Question 22

Question 29

Question 54

Question 52

Question 37

Question 17

Question 33