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Can you Give an example of bounded function which is not Riemann integrable?
Yes. A well-known example is the function defined as: f(x) = * 1, if x is rational * 0, if x is irrational Since this function has infinitely many discontinuities in any interval (it is discontinuous in any point), it doesn't fulfill the conditions for a Riemann-integrable function. Please note that this function IS Lebesgue-integrable. Its Lebesgue-integral over the interval [0, 1], or in fact over any finite interval, is zero.
What restrictions are there on the range of the function of H(w)?
That depends on how the function is defined.
What is an example of a function that is continuous on the interval a b for which the conclusion of the mean value theorem does not hold?
Let f(x)=abs(x) , absolute value of x defined on the interval [5,5] f(x)= |x| , -5 ≤ x ≤ 5 Then, f(x) is continuous on [-5,5], but not differentiable at x=0 (that is not differentiable on (-5,5)). Therefore, the Mean Value Theorem does not hold.
Does the graph of and odd function have to contain the origin?
No function ever really has to contain the origin if you constrain the domain to not include zero. Another way would be to just start graphing at x=1 and continue increasing x. In fact, you don't even have to graph at all since an odd function is defined as f(x) + f(-x) = 0
Which best describe the domain of a function?
The set of values for which the function is defined.
Can you Give an example of bounded function which is not Riemann integrable?
Yes. A well-known example is the function defined as: f(x) = * 1, if x is rational * 0, if x is irrational Since this function has infinitely many discontinuities in any interval (it is discontinuous in any point), it doesn't fulfill the conditions for a Riemann-integrable function. Please note that this function IS Lebesgue-integrable. Its Lebesgue-integral over the interval [0, 1], or in fact over any finite interval, is zero.
What is a perfect interval and how is it defined in music theory?
A perfect interval in music theory is a type of interval that is considered to have a strong and stable sound. It is defined as an interval that is either a unison, fourth, fifth, or octave, and has a specific number of half steps between the two notes.
Define upper and lower sums?
Let P = { x0, x1, x2, ..., xn} be a partition of the closed interval [a, b] and f a bounded function defined on that interval. Then: * the upper sum of fwith respect to the partition P is defined as: U(f, P) = cj (xj - xj-1) where cj is the supremum of f(x)in the interval [xj-1, xj]. * the lower sum of f with respect to the partition P is defined as L(f, P) = dj (xj - xj-1) where dj is the infimum of f(x) in the interval [xj-1, xj].
The time interval of 365.242 days is defined as the?
Tropical year
What is the number of values that lie in an interval?
The number of values that lie in an interval depends on the specific range and how it is defined. Generally, it can vary from zero values to an infinite number of values within the interval.
Determine which is the graph of the function Here is the equation httptinyurlcom4bzq4m Here is choice's 1-2-3-4 httptinyurlcom49u2og httptinyurlcom3ernxz httptinyurlcom5xkelp httptinyurlcom4g8r4q?
The question was, let f(x) = 2x if x < -2, ...2x - 2 if -2 <= x <= 2, and ...-2 if x < -2; and what is its graph. You might call this a piecewise-defined linear function. The easiest way to determine this is to look at each interval and see: * Is the function a straight line on each whole interval? * Can you pick two points on each interval so that they match the equation? * And is it a function? Do that and you'll be able to tell. E-mail me if you have more questions on this.
How do you determine the relative minimum and relative maximum values of functions and the intervals on which functions are decreasing or increasing?
You take the derivative of the function. The derivative is another function that tells you the slope of the original function at any point. (If you don't know about derivatives already, you can learn the details on how to calculate in a calculus textbook. Or read the Wikipedia article for a brief introduction.) Once you have the derivative, you solve it for zero (derivative = 0). Any local maximum or minimum either has a derivative of zero, has no defined derivative, or is a border point (on the border of the interval you are considering). Now, as to the intervals where the function increase or decreases: Between any such maximum or minimum points, you take any random point and check whether the derivative is positive or negative. If it is positive, the function is increasing.
The meter is defined as?
A meter is currently defined as the length of the path travelled by light in vacuum during a time interval of 1 / 299,792,458 of a second.
Why root 2 is smaller than 3 root 4?
This is because the square root function, with the range defined as the non-negative real numbers, is monotonic increasing throughout.
What is a function statement?
A function statement is a block where the function is declared and defined.
If a function is equal to zero when x is zero is the function considered defined at that point?
Yes, if the function is equal to zero at x=0, the function is considered defined at that point. The function's value at x=0 does not impact its overall definition.
What is continuous variate?
A variable defined on a continuous interval as opposed to one that can take only discrete values.
