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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
Clarify. Subtract four consecutive numbers ... from what?
It appears you mean something like:
22
- 21
- 20
- 19
And the answer is NOT -44.
It is -38 ... negative double of the LOWEST number.
If this is what you mean, then you have discovered another rule of mathematics. It will always work.
1001
- 1000
- 999
- 998
= -1996
Exactly the negative double of 998
What is the answer to 3 yards plus 1 feet?
3 yards plus 1 feet equals '10 feet' because there are 3 feet in 1 yard
Why is an empty set a subset of every set?
Because every member of the empty set is also a member of the other set. "If x is an element of the empty set, then it is also an element of the other set." Because the first part of the "if" is always false, the result is true. If this doesn't seem logical, see the Wikipedia article on "Vacuous truth".
What is a sentence for unit rate?
the unit rate of this problem that we need to find our deals with 1
Is power set of singleton set equal to null set?
No. Let A = {a} (a singleton set)
then
P(A) = {a, 0}
where 0 is the null (empty) set.
How is xex and xe2x integrated manually?
The definite integral of the function f=x*exp(k*x) is (1/k)*(x-(1/k))*exp(k*x). So you have the answer to your questions by setting k equal to 1 then 2.
I derived my formula by using integration by parts, setting u=x and dv=exp(k*x)dx.
Light travels at the speed of 186,000 miles per second. A light year is the distance light travels in one year. It takes 8 minutes for light to travel from the sun to the earth.
How can you determine when a function is increasing or decreasing?
Assuming the function is linear, the direction of the function can be determined by the coefficient's sign:
[y = mx + b]
Where m is the coefficient of x, if m is negative, then the function is increasing. If m is positive, the function is decreasing (this relationship is rather complicated and requires advanced calculus to prove).
