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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 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).
The number of permutations of the letter SUM is 3 factorial, or 6. Since none of those letters are repeated, the issue of repetition is not a factor. Perhaps the questioner meant to use a different word. If so, please restate the question.
How many liters is 1811 kilo liters?
1 kiloliter=1000 liters
1000x1811=1811 kiloliters
1,811,000 liters=1811 kiloliters.
How much does 1 sheet of 80gm paper weigh?
The area of A0 is 1 metre2. A1 has half that area, A2 is a half of A1, and so on. Thus the area of A4 is 1/16 m2.
If the paper has a mass of 80 grams per m2 then 1 sheet of A4 will have a mass of 5 grams.
How do you solve 3 multiplied by x plus 4 in a parentheses plus x?
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Answer 2(3x + 4) + x = yAssuming x = zero, then y = 4
Assuming x = 1, then y = 8
Assuming x = 2, then y = 12
Why is ten subtracted by zero equals ten but zero divided by ten equals zero?
10 - 0 = 10 because any number minus 0 is itself.0/10 = 0 can be rearranged to make more sense:
0 = 0*10 (multiply both sides by 10)
0 = 0 (logical conclusion)
therefore, 0/10 = 0 is true.
In fact, this also proves that 0/anything = 0.
How can two thirds of a hundred equal zero?
One way is if it was 100 zeroes. Another way is that given 100 has 3 digits, two thirds of the digits could be the two zeroes: "00". That would also enable the answer to be "10" or "01", so you have two other possible questions and answers.
