The derivative of digital function is defined in terms of difference. Then, which of the following defines the first order derivative ∂f/∂x= ___________ of a one-dimensional function f(x)?

The derivative of digital function is defined in terms of difference. Then, which of the following defines the second order derivative ∂2 f/∂x2 = ___________ of a one-dimensional function f(x)?

A

f(x+1)-f(x)

B

f(x+1)+ f(x-1)-2f(x)

C

All of the mentioned depending upon the time when partial derivative will be dealt along two spatial axes

D

None of the mentioned

Assertion (A): It is observed that step function is first derivative of a ramp function and impulse function is first derivative of a step function. Reason (R): From the derived time response expression it is concluded that the output time response also follows the same sequence as that of input functions.

A

Both A and R are true and R is the correct explanation of A

B

Both A and R are true but R is not correct explanation of A

C

Both A is True but R is false

D

Both A is False but R is true

First order derivative can enhance the fine detail in the image compared to that of second order derivative.

A

True

B

False

What kind of relation can be obtained between first order derivative and second order derivative of an image having a on the basis of edge productions that shows a transition like a ramp of constant slope?

A

First order derivative produces thick edge while second order produces a very fine edge

B

Second order derivative produces thick edge while first order produces a very fine edge

C

Both first and second order produces thick edge

D

Both first and second order produces a very fine edge

What kind of relation can be obtained between first order derivative and second order derivative of an image on the response obtained by encountering an isolated noise point in the image?

A

First order derivative has a stronger response than a second order

B

Second order derivative has a stronger response than a first order

C

Both enhances the same and so the response is same for both first and second order derivative

D

None of the mentioned

What kind of relation can be obtained between the response of first order derivative and second order derivative of an image having a transition into gray-level step from zero?

A

First order derivative has a stronger response than a second order

B

Second order derivative has a stronger response than a first order

C

Both first and second order derivative has the same response

D

None of the mentioned

The derivative of the symmetric function drawn in given figure will look like
Calculus mcq question image

A

B

C

D

Which of the facts(s) is/are true for the first order derivative of a digital function?

A

Must be nonzero in the areas of constant grey values

B

Must be zero at the onset of a gray-level step or ramp discontinuities

C

Must be nonzero along the gray-level ramps

D

None of the mentioned

If a programmer defines a class and defines a default value parameterized constructor inside it. He has not defined any default constructor. And then he try to create the object without passing arguments, which among the following will be correct?

A

It will not create the object (as parameterized constructor is used)

B

It will create the object (as the default arguments are passed)

The Fourier series of a real periodic function has only
P. Cosine terms if it is even
Q. Sine terms if it is even
R. Cosine terms if it is odd
S. Sine terms if it is odd
Which of the above statements are correct?

A

P and S

B

P and R

C

Q and S

D

Q and R

The derivative of digital function is defined in terms of difference. Then, which of the following defines the first order derivative ∂f/∂x= ___________ of a one-dimensional function f(x)?

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