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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 do you represent 10 oz into 1 lb in a fraction?

10 ounces equals 10/16 pounds. You can simplify the fraction if you wish.

Why is 1.3 less than 12?

12 is 10.7 larger than 1.3

12 is 1 less than 13

the decimal point makes 1.3 just over 1

What is recursive function?

A recursive function is one in which the value of a function at each point depends on its value at one or more previous points. A rercursive function requires the first few values to be defined normally - these are called bases.

Perhaps one of the most famous recursive function is the Fibonacci series, which has

f(1) = 1

f(2) = 1

f(n) = f(n-1) + f(n-2) for n = 3, 4, 5, ...

There are two bases and each subsequent value is defined in terms of the preceding two.

How do you find roots of z5 using demorves theorem?

z5 is an expression, not an equation and so cannot have roots.

What if you add a large positive number with a small negative number - Which sign will the answer have ... Positive or Negative?

If you have MORE positive amounts, than you have negative amounts, then the balance is a POSITIVE result. So answer is POSITIVE.

Think of it like this:- -6+9 is the same thing as +9-6, and, 9minus 6 = 3 but we only bother with the 'sign' if the amount is a negative amount, so 3 always means +3

Is googleplex infinity expressed in numbers?

No. Googleplex is a large number, but it is tiny in comparison to other numbers and trivially small in comparison to infinity.

What makes bandages stick?

Bandages stick to the skin because of the adhesive material on one side of the bandage. This adhesive is specially designed to create a bond with the skin's surface, providing a secure hold. The adhesive is non-toxic and hypoallergenic to prevent any irritations.

Are metals strongly attracted to magnets?

Most metals are not attracted to magnets at all. Some are, like:

Iron, Steel Stainless, Steel, Brass, Zinc, Copper, Bronze, Aluminum, Silver, Gold, Mercury, Nickel, & Magnesium.

Why isn't game theory taught in highschools?

I don't know, probably because the average high school curriculum is too narrow to allow topics such as game theory, abstract algebra (such as Lie algebra), complex analysis, or projective geometry.

Why is 4 a good number?

Well the number 4 is actually my lucky number but it's nit a good number to every one just some people

But people do believer it's a good number because it's a small even number and can be divided, be the divider and because it takes slot of part with fractions which you use a lot in life

Why do you use integral calculus?

If we have to find the volume of a cylinder then we could imagine as if slices of same size have been mounted one over the other and knowing volume of one piece we could find the entire volume just by multiplying by an integer.

But in case of cone, as we put them into thin slices of thickness dx then volume of each would differ as the radii are different for different slices. Hence we need integral calculus with which we could easily get the right formula 1/3 pi r2 h with base radius r and height h

What are all of the numbers less than 100 that are the product of exactly 3 different prime numbers?

Take your pick from: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 and 97 which are all prime numbers less than 100

What is the equation for orthocenter?

The orthocentre of a triangle is the point at which the altitudes meet.

In what components dot and cross product resolve?

A dot product is a scalar product so it is a single number with only one component. A cross product or vector product is a vector which has three components like the original vectors.

State the characterictics prime numbers share?

The crucial importance of prime numbers to number theory and mathematics in general stems from the fundamental theorem of arithmetic.