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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 do you call the simplest function within a family of functions?
f(x) = 0 or 1 are probably the simplest.
One over four divided by negative two over five?
The answer to 1/4 divided by -2/5 equals -0.025. This is a math problem.
How do you convert percentages into averages?
Are you talking about grades? There are several ways to do this. Ask the teacher how it is done.
What are the essential elements of modern day statistics?
Modern day statistics involves the collection, organization, interpretation and the resulting presentation of numerical information.
What is the probability of landing a tails on the third toss of the coin?
It's 50/50 with an honest coin except for the Kennedy half dollar.
Do you need math to be a composer?
Yes, being a composer requires vast knowledge of musical notes and times (4/4ths time, etc) each note has a specific amount of time a lotted to it's beat (4 quarter notes per bar)... etc.
Why is it said that if you add percents you often obtain incorrect results?
It may refer to the sum of percentages using 'whole number' approach.
For instance:
In a class A of 20 students only two students are redheaded, i.e. 10% of the students are redheaded. In a class B of 30 students only three students are redheaded, i.e. 10% of the students are redheaded. All students of the class A and all students of the class B are in assembly hall. What is the percentage of redheaded student in the assembly hall?
To answer the question the sum of both class percentages (10%+10%=20%) cannot be used.
You cannot even express the class percentages in fractions and sum them (10/100 + 10/100=20/100=20%).
The easiest way to calculate the percentage of the redheaded students in the assembly hall is to calculate the percentage from scratch ((2+3)/(20+30)=0.10=10%) and not to use the class percentages.
Another example of problem with the summation of percents are consequent percentage changes.
The book you want to buy was marked off 30%. Afterwards the book was discounted by 30% again. If you buy the book after the second discount, you save 51% of the original price (not 60%, the sum of the two discounts).
The first discount reduced the price to 70% of the original price. The second discount reduces the discounted price by 30%, i.e. the final price is 49% of the original price (0.7*0.7=0.49=49%). You save 51% (100%-49%).
Percentage decrease followed by percentage increase can cause even more surprising results.
The price of a share decreased by 60% one year. The next year the share price raised by 80%. The net effect was 28% decrease from the original price!
The share price was 40% of the original price after the first year. The next year the price raised by 80% of the lowered price, i.e it was 72% of the original price (1.8*0.4=0.72=72%). The net decrease was 28% (72%-100%).
What is the slope of a line containing the points 2 2 and 4 2?
The Slope of a line containing the points (2,2) and (4,2) is
Y=0
500 ml = 1/2 liter
so, two times of 500 ml make one liter.
How do you write 36.678 in word form?
Thirty-six point six seven eight.Or thirty-six and six-hundred seventy eight thousandth.
What is a 'unit'? A unit could be one pint, then the answer is 1000. Or one un it could be a quart, then the answer is 500.
Iteration is a process where you use your previously obtained answers in your next equation. Consider the equation x_(n+1)=x_(n)+4. Where n is an arbitrary non negative integer.
We must be given an original x_0 say x_0=1 here. Then
x_1=x_0+4=5
x_2=x_1+4=9
x_3=x_2+4=13
and so on....
What is the difference between the primal and dual?
The difference between primal and dual are that primal means an essential, or fundamental of an aspect where as dual means consisting of two parts or elements. Primal is one, dual is two.
71 : Python code that demonstrates this.
N = 1 while True : if N % 8 8 : print N break N += 1
It is a length measure that equals 200 centimeters
1 foot = 0.3048 meters = 12 inches
so, 2 meters = 2/0.3048 feet = 6.56 feet or = 6 feet 6.72 inch
How do you write one hundred eighty six thousand in numbers?
It is 186.000 miles per hour using measurement units which are used mainly in the US. In miles per second, this is the speed of light in vacuum. Although the English (technically the British) do use miles to measure distance, the speed of light is a scientific measure and the British would use kilometres per second as the appropriate measurement units.
How do you define a metric space through the use of sets?
The concept of a distance, or metric, between the elements of a set is well defined in topology. Let B be any set with x, y, z Є B, and let D be a function from the Cartesian product, B X B, into the set of real numbers, R. D is called a metric on B if the following four statements hold:
1) D(x,y) ≥ 0 for all x, y
2) D(x,y) = D(y,x) for all x, y
3) D(x,y) = 0 if and only if x = yfor all x, y
4) D(x,y) + D(y,z) ≥ D(x,z) for all x, y, z
In this case, the set B having metric D is called a metric space, and is often notated as B, D.
For more information and related definitions, see the links below.
