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Mathematical Analysis
Mathematical analysis is, simply put, the study of limits and how they can be manipulated. Starting with an exhaustive study of sets, mathematical analysis then continues on to the rigorous development of calculus, differential equations, model theory, and topology. Topics including real and complex analysis, differential equations and vector calculus can be discussed in this category.
2,575 Questions
How can you tell when a fraction with prime denominator terminates and when it repeats?
If the denominator is 2 or 5 it terminates. Otherwise it repeats.
What is the principle of differentiation?
Differentiation of funtion is rate of chnage of that funtion.
How do i write three tenths as a decimal and in expanded form?
It is 0.3 in decimal form. There is no further expanded form.
Calculus is the study of functions based on the premise that all smooth curves can be considered to consist of infinitesimally small straight segments (microsegments). One consequence of this premise is that arbitrary values on the generic microsegment are nilsquare (equal to zero when squared). This applies most obviously to the values of the microsegment around zero in y = x^2. Another consequence is that the applicable logic omits the law of excluded middle; that is, it would be false to say that an infinitesimal is either identical to or distinct from zero.
Thus for any smooth curve,
f'(x) = [f(x+E) - f(x)] / E
Where f'(x) indicates the rate of change of the function and where E (epsilon) is an infinitesimal microsegment. The process of working out rates of change is called Differentiation. The most useful form of the above equation is,
f(x + E) = f(x) +Ef'(x)
If the area beneath a curve between the origin and x is given by A(x) then,
A(x + E) = A(x) + EA'(x)
We also independently know that,
A(x + E) - A(x) = Ef(x) + 1/2f'(x)E.E
The second term on the RHS is the triangle beneath the microsegment and the first is the rectangle beneath that. Combining these equations, removing the null term, and cancelling E yields,
A'(x) = f(x)
This is the Fundamental Theorem of Calculus. It shows that the reverse differentiation of a function yields its area function. This process is called Integration. The name of the approach to calculus outlined here is Smooth Infinitesimal Analysis.
its a type of math that involves algebra and trigonometry.
The branch of mathematics that deals with limits and the differentiation and integration of functions of one or more variables.
Calculus is a math figure relating to targeting an object. Below is an example of calculus:
You are about to shoot a missile at plane. The plane is moving forward a little bit, so you aim in front of the plane so that the missile and plane collide.
NOTE: Calculus does not count as a mathematical figure if the "Missile" is Target-Locked. Calculus only counts if the "Missile" Is aiming ahead of the "Plane" to intercept. Target-Locking "Missiles" allways aim for the "Plane" and collide with it.
Application set theory on business section?
Set theory does have many practical business applications. Some of these include how the Turing machine is used in computer science, and the theory of crisis of foundations in math.
A line of symmetry (let us call it LoS, for short) defines a boundary where the object in view is the same on both sides of the boundary. The easiest way to visualize an LoS will be draw a random figure on a piece of paper on a table -- an oval perhaps. Take a rectangular mirror and place it within the figure. The portion of the figure that you can see from the glass side of the mirror (not the opaque side) is an exactly replica of the image you see in the mirror. The line where the mirror meets the paper forms an LoS.
In the real world, some objects have LoS's. Most mechanical parts are drawn to be symmetric, for example, so one can make them on a lathe. Electrical circuits can have symmetry too. Same for chemistry -- the molecular structure for H2O, CO2 or CH4, for example. The usefulness of an LOS is that since the portion on one side of the LoS is identical to one on the opposite side, one needs only to treat (calculate area, amount of material to use, measure the angle etc.) one side and assume the same for the other side, reducing the effort for the task.
What is a simple interest in math?
Simple interest is interest that is calculated only on the amount of unpaid principal on a loan. Such interest is not added to the value of the loan but is tracked separately.
Compound interest is interest that is calculated on the total of unpaid principal and accumulated interest on a loan.
The difference is in simple interest there is no interest charged on accumulated interest while in compound interest there is interest charged on accumulated interest.
How can you count the maximum number of license plates a state can issue?
First you need to know the rules like:
- There are never the letter O as All Os are Zeros
- Do all the first digits need to be Letters
- How many digits must there be, Where I live currently 7 letters or numbers
- Can there be vanity plate of all letters and do they need to conform to the other rules?
When you know all the rules:
- How many letters, and how many places can they be used
- How many numbers can be used and where in the sequence
- Where are the gaps or dashes and how must they be used.
This example is not correct, you need to figure yours out for yourself based on your homes rules: Formula is ( Letters X allowed positions ) X ( Number of numbers X allowed positions.) and that could be X number of position that could be either numbers or letters.
Is it possible for a finite set to have the same cardinality as its power set?
No.
If the cardinality of a finite set is N, then that of its power set is 2N. These cannot be equal for any non-negative integer N.
What is meant by bimodal distribution?
You are likely familiar with the probability density function of the normal distribution--that is, the bell-shaped curve.
A bimodal distribution is one whose probability density function has two 'humps' or maxima. In other words, values of the random variable are more likely to occur around where those two maxima occur than elsewhere, in the same way that values of a normally distributed random variable are more likely to occur around its maximum.
half of 627 is 313 1/2. Three hundred and thirteen and a half.
What is the range of the function 1 2 2 4 3 6 4 8?
The smallest number is 1 and the largest number is 8. The range is the largest minus the smallest, so it is 8-1=7.
Why do men find it so hard to apologize?
It's just not men that have this problem, but I've had many female friends that don't apologize, but try harder in our relationship. Sometimes we just have to accept that. As long as the person tries to change (without apology) and things are running more smoothly that's all that matters. Some men detest confrontations and it shows up in the business world and many other aspects of life. (eg: two female employees in a snit and the male boss or supervisor hits the floor!) Men have had it driven into their heads from the beginning of time that they should be wise, strong, protect those around them they love and that's one tall order. To apologize is an admission they didn't do a very good job. They want to seem tough.
Zero
any number instead of 4 like 1234567890 and it will still be ZERO!!!!!!!!!!!!
How do you write in words of 637 657 square kilometers?
Six hundred and thirty-three thousand, six hundred and fifty-seven square kilometers.
