0
A 1-dimensional interval (a, b) is continuous if for any k in (0, 1) the point a + k*(b-a) = a*(1-k) + k*b is also in the interval.
This is equivalent to the statement that every point on the line joining a and b is in the interval.
The above can be extended to more dimensions analogously.
What else can I help you with?
Is a function that is continuous over a finite closed interval not have a maximum or a minimum value over that interval?
A function that is continuous over a finite closed interval must have both a maximum and a minimum value on that interval, according to the Extreme Value Theorem. This theorem states that if a function is continuous on a closed interval ([a, b]), then it attains its maximum and minimum values at least once within that interval. Therefore, it is impossible for a continuous function on a finite closed interval to not have a maximum or minimum value.
What is continuous variate?
A variable defined on a continuous interval as opposed to one that can take only discrete values.
Is GPA interval data?
Yes, it is a Continuous variable measured along an equidistant scale.
Linear discrete time signal?
The linear discrete time interval is used in the interpretation of continuous time and discrete valued: Quantized signal.
What does an interval look like?
An interval in mathematics is a set of numbers that contains all numbers between any two numbers in the set. It can be represented on a number line as a continuous section between two points, often denoted in notation such as [a, b] for a closed interval (including endpoints a and b) or (a, b) for an open interval (excluding endpoints). Intervals can also be infinite, like (-∞, b) or (a, ∞). Visually, an interval appears as a line segment or ray depending on its type.
Is it true that a continuous function that is never zero on an interval never changes sign on that interval?
Yes.
What is continuous variate?
A variable defined on a continuous interval as opposed to one that can take only discrete values.
What kind of continuous function can change sign but is never zero?
If the function is continuous in the interval [a,b] where f(a)*f(b) < 0 (f(x) changes sign ) , then there must be a point c in the interval a<c<b such that f(c) = 0 . In other words , continuous function f in the interval [a,b] receives all all values between f(a) and f(b)
Is GPA interval data?
Yes, it is a Continuous variable measured along an equidistant scale.
Is land area interval variable?
Yes, land area is considered an interval variable because it can be measured on a continuous scale with equal units between values.
Prove that if the definite integral is continuous on the interval ab then it is integrable over the interval ab sorry that I couldn't type the brackets over ab because it doesn't allow?
why doesn't wiki allow punctuation??? Now prove that if the definite integral of f(x) dx is continuous on the interval [a,b] then it is integrable over [a,b]. Another answer: I suspect that the question should be: Prove that if f(x) is continuous on the interval [a,b] then the definite integral of f(x) dx over the interval [a,b] exists. The proof can be found in reasonable calculus texts. On the way you need to know that a function f(x) that is continuous on a closed interval [a,b] is uniformlycontinuous on that interval. Then you take partitions P of the interval [a,b] and look at the upper sum U[P] and lower sum L[P] of f with respect to the partition. Because the function is uniformly continuous on [a,b], you can find partitions P such that U[P] and L[P] are arbitrarily close together, and that in turn tells you that the (Riemann) integral of f over [a,b] exists. This is a somewhat advanced topic.
Is skin temperature in degrees centigrade interval data?
Yes, skin temperature in degrees centigrade is considered interval data. Interval data is continuous data that has a meaningful zero point, but ratios between values are not meaningful. Skin temperature can be measured on a continuous scale with a specific unit of measurement (degrees centigrade) where a value of zero does not indicate absence of skin temperature.
What part of a map allows you to determine the type of information it contains?
The contour interval
How can you determine whether an interval is major or minor?
You can determine whether an interval is major or minor by counting the number of half steps between the two notes. If the interval has a distance of 2, 3, 6, or 7 half steps, it is major. If it has a distance of 1, 4, 5, or 8 half steps, it is minor.
Is there a formulaic method of finding the number of real roots of an arbitrary continuous function over a specified interval?
sorry but are gone mad
Difference between interval training and continuous training?
Interval training is periods of work followed by periods of rest. This is known as work:rest ratio. This is commonly used to train the anaerobic energy system. Continuous training, of which there are many forms does not involve rest periods, although it could involve periods of different intensities (such as Fartlek training).
What are the 5 different types of training used for training in netball?
well there is weight training, fartlek,continuous, interval , circuit, flexibility and weight
