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The inverse image of measurable set is measurable?
Possibly under certain conditions, but not generally. Consider a nonmeasurable set A, and define f(x) = 1 if x in A 0 otherwise. Then {1} is certainly measurable but the inverse image {x | f(x) = 1} = A is not measurable.
Is work function is constant?
No.
What is the significance of the first derivative of a function to be a constant?
If the first derivative if a function is a constant that the original function has only one slope across its entire domain, so it is a line.
What is the derivative of the the constant function?
zero
Why does an answer to an integration problem involve a Constant of Integration?
The indefinite integral is the anti-derivative - so the question is, "What function has this given function as a derivative". And if you add a constant to a function, the derivative of the function doesn't change. Thus, for example, if the derivative is y' = 2x, the original function might be y = x squared. However, any function of the form y = x squared + c (for any constant c) also has the SAME derivative (2x in this case). Therefore, to completely specify all possible solutions, this constant should be added.
If constant function is measurable then is it necessary that domain is measurable?
yes.since this functin is simple .and evry simple function is measurable if and ond only if its domain (in this question one set) is measurable.
What is an example of a simple borel measurable function?
Characteristic function of any borel set is an example of simple Borel function
The measurable quantities of the gases at equilibrium must be?
constant
What is a function defined by an equation of the form ykx where k is a nonzero constant?
Set of instruction are known as function.
What is function of capacitor in 555 IC?
the capacitor and its associated resistor set the time constant.
The inverse image of measurable set is measurable?
Possibly under certain conditions, but not generally. Consider a nonmeasurable set A, and define f(x) = 1 if x in A 0 otherwise. Then {1} is certainly measurable but the inverse image {x | f(x) = 1} = A is not measurable.
The rate of change of any nonlinear function is constant?
No. Only a linear function has a constant rate of change.No. Only a linear function has a constant rate of change.No. Only a linear function has a constant rate of change.No. Only a linear function has a constant rate of change.
Is utility constant along a demand curve?
utility is not constant along the demand curve
Can you replace a formula with its function so it can remain constant?
No but if you replace a constant with a function it will remain a formula
Can you replace a formula with its function so it remains constant?
No but if you replace a constant with a function it will remain a formula
How would you prove that there are no closed contours in the contour plot of a harmonic function?
This is not exactly true as a constant function is harmonic and has closed contours as its contour plot (i.e. the entire plane is closed). However, any function that has closed contours can be shown to be the constant function. Here is how. If, say u, is a harmonic function which is constant on a contour which is closed, then the inside of that contour is a domain (simply connected set if that has any meaning to you). By the maximum and minimum principles respectively, the function u must attain both its max and min on the boundary i.e. the contour. This number is a constant and since the maximum is the same as the minimum we can conclude that the entire function is constant on the insides of the contour. From there we can extend this function to the entire plane by identity principle.
What is the definition of a linear function?
a linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable.
