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.
No.
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.
zero
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.
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.
One example of a simple Borel measurable function is the indicator function of a Borel set. This function takes the value 1 on the set and 0 outside the set, making it easy to determine its measurability with respect to the Borel sigma algebra.
Set of instruction are known as function.
constant
the capacitor and its associated resistor set the time constant.
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.
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.
utility is not constant along the demand curve
No but if you replace a constant with a function it will remain a formula
A constant function is a function that always yields the same output value, regardless of the input. In other words, the function's output is a fixed value and does not depend on the input variable. Graphically, a constant function appears as a horizontal line.
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.
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.