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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 place and face values of 4 in 324372?
It is in the 1000's place and its face value is 4000
Is zero divided by zero equal to zero?
Actually 0/0 is undefined because there is no logical way to define it. In ordinary mathematics, you cannot divide by zero.
The limit of x/x as x approaches 0 exists and equals 1 so you might be tempted to define 0/0 to be 1.
However, the limit of x2/x as x approaches 0 is 0, and the limit of x/x2 as x approaches 0 does not exist .
r/0 where r is not 0 is also undefined. It is certainly misleading, if not incorrect to say that r/0 = infinity.
If r > 0 then the limit of r/x as x approaches 0 from the right is plus infinity which means the expression increases without bounds. However, the limit as x approaches 0 from the left is minus infinity.
What are the domain and range of y equals ex plus 2 - 1?
I would suggest you plot it using, say GeoGebra. (Very easy to use.) On the left side of the y-axis the graph never falls below y=-1, I think. It climbs indefinitely on the right side. It extends indefinitely to the left, and to the right. But, as I say, if you learn GeoGebra, many problems like these will become much easier.
What is the perfect number less than 40?
The two perfect numbers less than 40 are 6 (1+2+3) and 28 (1+2+4+7+14).
Yes Because 46 is a even number because it has 6 at the back of it.
How much topsoil do you need to fill an area 24feet long 8 feet wide and 16 inches deep?
The easiest way to calculate the amount of topsoil you'll need is to multiply the totals together to get the cubed feet.
If you notice you have two units of feet and one of inches. Since 16 inches is over one foot but less than two feet you'll still have to purchase an additional bag of topsoil to cover the extra 4 inches. So let's just round the 16 inches up to 24 inches or 2 feet.
24 ft x 8 ft x 2 ft = 384ft³.
What is TOPSIS method in Multi-criteria Decision making?
it stand for Technique For Order preference BY Similarity to Ideal Situation
The principle behind TOPSIS is simple: The chosen alternative should be as close to the ideal solution as possible and as far from the negative-ideal solution as possible. The ideal solution is formed as a composite of the best performance values exhibited (in the decision matrix) by any alternative for each attribute. The negative-ideal solution is the composite of the worst performance values. Proximity to each of these performance poles is measured in the Euclidean sense (e.g., square root of the sum of the squared distances along each axis in the "attribute space"), with
optional weighting of each attribute.
How do you get to the third side of a hexa-flexagon?
The flexagon will keep traversing from one side to the next in a loop.
There are other types of flexagons that will go between multiple sides.
These can be diagramed by the tuckerman traversal
3.25 divided by 4 (the quarter) is:
13/4 * 1/4 = 13/16 = 0.8125.
What is 23.535 as a mixed number in simplest form?
This is a bit of an awkward fraction.
Top heavy fraction: 4707/200
Mixed fraction: 23 and 107/200
How many words of 6 letters can be written if the first and last letters are both q?
6 letters minus your 2 unchanging letters leaves you with 4 letters of any combination of 26 possible characters each. That is 26^4 26 to the 4th. 456976 different combinations. If you understand permutations I used the simple repeatable permutations formula x^n.
What date will thanksgiving fall on in 3011?
You can work it out yourself - each date in the calendar repeats every 11 years. So - since the fourth Thursday in November this is the 24th - then the same date will be on the same day in 2022, 2033 & 2044. I'll leave you to do the rest !
