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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 are 26 geometrical properties each being in consecutive order of the alphabet?
Examples are as follows:-
Alternate angle
Bisector
Circumference
Diameter
Exterior angle
Face
Ground
Hexagon
Interior angle
Junction
Kite
Line segment
Mid-point
Nonagon
Octagon
Parallelogram
Quadrilateral
Rectangle
Square
Triangle
Undecagon
Vertex
Width
X- axis
Y-axis
Zone
* * * * *
You can look up these or more terms at the attached link.
Unfortunately, the browser used for posting questions is hopelessly inadequate for mathematics: it strips away most symbols. All that we can see is "...find Th and Th derivative of y - five cos (twox) ...". From that it is not at all clear what the missing symbols (operators) might be. I am guessing that you want the nth and (n+1)th derivatives of something like y = -5*cos(2x). I am also assuming that you are familiar with the chain rule for finding derivatives. Finally, this browser is also rubbish and I cannot show superscripts so I will use the ^ symbol to represent powers..
y = -5*cos(2x)dy/dx = -5*[-sin(2x)]*2 = 2*5*sin(2x) d^2y/dx^2 = 2*5*cos(2x)*2 = 2^2*5*cos(2x)d^3y/dx^3 = 2^2*5*[-sin(2x)]*2 = -2^3*5*sin(2x) d^4y/dx^4 = -2^3*5*cos(2x)*2 = -2^4*5*cos(2x) = 2^4*y
So,for n = 1, 5, 9 ... [n = 1 mod(4)]: d^ny/dx^n = 2^n*5*sin(2x) = 2^n*5*cos(pi/2 - 2x)for n = 2, 6, 10 ... [n = 2 mod(4)]: d^ny/dx^n = 2^n*5*cos(2x) = -2^n*y
for n = 3, 7, 11 ... [n = 3 mod(4)]: d^ny/dx^n = -2^n*5*sin(2x) = -2^n*5*cos(pi/2 - 2x)
for n = 4, 8, 12 ... [n = 0 mod(4)]: d^ny/dx^n = -2^n*5*cos(2x) = 2^n*y
q = k*r^3/(s*sqrt(t))
Why is a math variable a lowevercase letter?
Sometimes it is, sometimes it is not. There is no rule or even a convention, about it.
What is another set of values the helps describes variability in a data set?
The word "another" in the question implies that you already have one or more set of values in mind. However, you have not chosen to share that information. It is, therefore, impossible for me to know whether the answer that I suggest is already one that you know of or a new one.
The word "another" in the question implies that you already have one or more set of values in mind. However, you have not chosen to share that information. It is, therefore, impossible for me to know whether the answer that I suggest is already one that you know of or a new one.
The word "another" in the question implies that you already have one or more set of values in mind. However, you have not chosen to share that information. It is, therefore, impossible for me to know whether the answer that I suggest is already one that you know of or a new one.
The word "another" in the question implies that you already have one or more set of values in mind. However, you have not chosen to share that information. It is, therefore, impossible for me to know whether the answer that I suggest is already one that you know of or a new one.
It is 12 feet tall - as stated in the question!
Prime Factorization:
72= 2x2x2x3x3
44=2x2x11
GCF: 2x2 =4
LCM: 2x2x2x3x3x11=792
Nope. The Ancient Greeks were trying to find the ratio of circumference to area.
9729 is evenly divisible by 9. 9729 divided by 9 equals 1081.
What are the rules for integration?
There are a lot of rules for integration! Plus a lot of techniques!
Here is the power rule as a simple example.
int[Xn dx]
= (Xn + 1)/(n + 1) + C
( n does not equal - 1 )
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.
