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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
What is the fourier transform of Tan function?
tanx = 2*(sin2x - sin4x + sin6x - ... )
However, be warned that this series is very slow to converge.
Does 6.66 equal 6 hours 46 minutes?
6.66 hours is 6 hours 39 minutes 36 seconds.
6.66 repeating is 6 hours 40 minutes.
What kind of statement has the form of 'if A then B' which means if a is true then b must be true?
An example of a conditional statement is: If I throw this ball into the air, it will come down.
In "if A then B", A is the antecedent, and B is the consequent.
Why is anything divided by zero equal to infinity?
Division by zero is undefined. Even dividing zero by zero is undefined. That's because there are no unique results. This derives from the identity function of zero, such that any value multiplied by zero is zero.
While the division of any number by a diminishing fraction has a limit of infinity, there is no reverse operation possible. I.e. for any nonzero number n:
If n/0 = ∞ it implies ∞ x 0 = n but any number times 0 = 0
and
If 0/0 = n then n could be any real number, not just 1, because n x 0 = 0
What is the use of studying theory of computation?
There are several uses. I will mention two.
One is to make calculations more efficient. For example, suppose you want to calculate x^2 + 2x + 4. Each operation is binary, that is, two inputs are converted to one output.
Option I
- calculate x*x
- calculate 2*x
- add them together = x*x + 2*x
- add 4 to the above.
or
Option II
- calculate x+2
- multiply by the above by x = x^2 + 2x
- add 4 to the above.
That saves 1 binary operation in the calculation. If such a calculation is carried out thousands - or millions - of times, this small difference can save a lot of time.
Second, it is important to understand the behaviour of computation errors. Most rational numbers and all irrationals have infinitely long decimal - or binary - representations. Computers cannot work with infinitely long strings of digits and so need to truncate the numbers. This leads to rounding errors and understanding these is crucial in understanding the accuracy and limitations of your calculations.
Is withdrawal an increase or decrease?
A withdrawal is a decrease because you are taking something away.
What is the multiply of 7 nearest to but greates than 10?
It is: 14 because 2*7 = 14 which is greater than 10
The left 7 represents 700. The right 7 represents 70. The left '7' is 10 times greater than the right '7'.
Assuming that all the cedar trees are the same and that the three apple trees are the same, and it doesn't matter which of the apple trees you purchase, then you have the following options: CCCCAAA, CCCCAA, CCCCA, CCCC, CCCAAA, CCCAA, CCCA, CCC, CCAAA, CCAA, CCA, CC, CAAA, CAA, CA, C, AAA, AA or A. This is 19 possibilities.
Because the problem says that you buy trees, the null set (i.e., not buying anyting) is not as option.
How many grams does an empty water bottle have?
The answer depends on how big the bottle is and what material it is made of.
That depends. Are all the positions equal, will they all just be members of the committee or will there be a chairman, vice-chairman, secretary, treasurer, etc.?
Assuming all are equal positions, then order of selection does not matter, then
(25x24x23x22x21x20)/(6x5x4x3x2x1) = 177,100
What is a statement that is always true forwards and backwards?
A bi-conditional statement can be true or false. If it is true, then both forward and backward statements are true. See Bi-conditional Statement
In English grammar
The statement, Love you! could be true too if said/written backward as You love!
How do you calculate the explicit formula and the nth term of the Fibonacci sequence?
(1/sq rt 5)((1+sq rt 5)/2)n - (1/sq rt 5)((1-sq rt 5)/2)n
This is based on the golden ratio (1+sq rt 5)/2) because the ratio of 2 Fibonacci terms approaches the golden ratio as the 2 terms used get larger. IE the ratio ot the 10th term to the 9th term is 55/34 = 1.61765 and the golden ratio is approx. 1.61803.
When using this formula if your calculator does not round, you will round to get the appropriate Fibonacci number.
What is optimal feasible solution?
It is usually the answer in linear programming. The objective of linear programming is to find the optimum solution (maximum or minimum) of an objective function under a number of linear constraints. The constraints should generate a feasible region: a region in which all the constraints are satisfied. The optimal feasible solution is a solution that lies in this region and also optimises the obective function.
