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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
Can you provide examples of successful people making it only after multiple failures?
Scott Adams (the successful creator of dilbert) wrote a whole book on this topic, called "stick to drawing comics, monkey-brain"
How many thousand crores in rs 5965000 lacs?
5965000 lakhs = 5.965 thousand crores.
5965000 lakhs = 5.965 thousand crores.
5965000 lakhs = 5.965 thousand crores.
5965000 lakhs = 5.965 thousand crores.
How can you reduce zero point zero zero two over a thousand?
0.002 = 2/1000 = 1/500
0.002/1000 = 2/1000000 = 1/500000
How much water will fit into a 10 x 1' steel pipe?
The volume of a cylinder is pi * r^2 * height. For a 10 foot pipe with a 1 foot internal diameter (1/2 foot radius), the volume is:
~ 3.1416 * (.5)^2 * 10 = 7.854 cu. ft. of water (or anything else)
If, as you approach the variable from either side, the value of the function increases without bound, then the limit of the function is infinity. More formally, the limit of a function, f(x) is infinity at x = z if, given any large number N you can find a number d such that f(x) > N for all x such that |x - z| < d.
In other words, you can always find an immediate neighbourhood of z, such that the value of the function is larger than any number you care to name.
There are several possible scenarios in which a limit may not exist. A common situation is when the limits are different depending on which direction you approach z from. For example, consider f(x) = 1/x and z = 0.
If you approach z from the positive side, then f(x) can be made larger than any large positive number: limit = + infinity. On the other hand, if you approach z from the negative side, f(z) can be made smaller than any negative number: limit = - infinity.
The limits need not be infinite. You could have a function defined as follows:
f(x) = 0 for 0 <= x < 1
f(x) = 1 for x >= 1
Approaching 1 from "below", the limit of f(x) is 0 while from "above", you get f(x) = 1. This kind of function - an indicator function- is quite common. For example, the presence of a current in a circuit if the power is switched on at time x = 1.
How do you solve 5xy plus 7xsquared - 12y when x equals 2 y equals 1?
In the given expression you replace x by 2 and y by 1.
Thus 5xy + 7x2 - 12y = 5*x*y + 7*x2 - 12*y
= 5*2*1 + 7*22 - 12*1 = 10 + 28 - 12 = 26
if two signal input fed into circuit and gating one output
What does the number 0408163245576318222527346277 mean?
It does not mean anything specifically. In a particular context it may have some meaning but you have chosen not to share that context with us.
At any given time in hours after the family departs, the distance they have travelled will be 60t, while at the same time, the moving van will have covered a distance of 55(t + 1). The family will catch up when these two times are equal, or when 60t = 55(t + 1), or 60t - 55t = 55, or 5t = 55, or t = 55/5 hours = 11 hours.
How much greater is 4 to the power of 2 than 4 to the power of negative 2?
4 to the power of 2 is 42 = 16
4 to the power of negative 2 is 4-2 = 1/42 = 1/16
As far as "how much greater" - that depends on what you mean
If you mean what is the size of the difference...
16 - 1/16 = 15 15/16 = 15.9375 so 4² is 15.9375 greater than 1/4²
If you mean the ratio...
42/4-2 = 44 = 256 so 42 is 256 times the size of 4-2 or 255 times bigger
(i.e. 42 = 4-2 + 255·4-2)
What if you fell 4 classes in 9 grade?
If you fail 4 classes you will still be classified as a 9th grader.
What numbers add to give you 8 but multiply to give you 36?
4 + 2i*sqrt(5) and 4 - 2i*sqrt(5)
[where i is the square root of -1]
Given a+b=8, we have b=8-a.
Given ab = 36, we can substitute b=8-a to get a(8-a) = 36, or
a2 - 8a + 36 = 0
Using the quadratic formula gives the two possible answers, which accounts for the fact that a and b can be switched without affecting the problem.
How do you apply laplace transform method to solve systems of ordinary DEs?
you apply the Laplace transform on both sides of both equations. You will then get a sytem of algebraic equations which you can solve them simultaneously by purely algebraic methods. Then take the inverse Laplace transform .
