To find a range you have to use logic and think of all the possible outputs. Generally sine, cosine, polynomials of even degrees, and absolute values are the only ones that aren't all real numbers. If they give you a set of Y values though, you simply list them (ex (1,2)(2,4) and (3,-5) have a range of {2,4,-5})
Lastly watch out for discontinuities such as in (X^2+5x)/(x+5) which may look like y=x except at -5 where there is no value. Therefore y never=5 so the range is all real numbers where x is not 5.
It was Archimedes.
Is hypotenuse is greater from other sides in Pythagoras theorem?
The hypotenuse is the longest side. In a right-angled triangle, the hypotenuse is always opposite the right angle.
What are concepts or rules made by Gottfried Leibniz?
leibniz uses the same basic concepts and rules as newton, no one knows who came up with them first,, chain rule, quotient rule,, but the only difference is that newton uses y prime(y') and leibniz uses the dy/dx ... personally i like newtons better, but when it comes to the quotient and chain rule leibniz is easier.
Who are the mathematicians on variation?
Assuming you mean "the calculus of variations," all the big names were involved in its development; Bernoulli, Euler, Lagrange, Legendre, Cauchy, Clebsch, Weierstrass, Hilbert, and Lebesgue to name a few.
What did Pythagoras do to celebrate when he discovered the theorem?
He sacrificed a goat, and celebrated with fellow pythagorians
Why must mersenne numbers be odd?
All Mersenne primes are one less than some multiple of two. Any multiple of two is even, so any multiple one less than a multiple of two must be odd.
How did Leonhard Euler's theory help mankind?
He was a very able mathematician and developed many theories. The question needs to be more specific. Which theory are you referring to?
Who tried to get the first calculation of pi?
The ancient Babylonians from around 1700 BC used pi = 3.125. The name of the person who calculated that value was not recorded.
What was Nicholas Copernicus remembered for?
Dude sat in his back yard and said "whoa those other dudes are wrong. The earth is moving around the sun, the sun isn't going around earth. Oops I shouldn't have figured that out, they are going to kill me."
What has the author Pierre de Fermat written?
Pierre de Fermat has written:
'Osservazioni su Diofanto'
'Bemerkungen zu Diophant'
'Varia opera mathematica Petri de Fermat' -- subject(s): Geometry, Early works to 1800, Number theory
'Oeuvres de Pierre Fermat' -- subject(s): Mathematics
If those grades are weighted equally, then no.
How does 1 over 3 to 100th power have a repeating or terminating decimal representation?
It is repeating. Any fraction in simplest terms which has ANY prime factor other than 2 or 5 in its denominator will be a repeating fraction.
How did René Descartes make his discoveries?
Rene Descartes was a philosopher, mathematician and scientist. He made several discoveries and unfortunately, your question does not specify which discovery you are referring to.
What did Leonhard Euler contibute in mathematics?
He made big contributions in graph theory, calculus and more. I have attached a link with lots of information about this amazing man.
What did joann carl fried rich gauss do to contribute to math?
Lots of stuff. Why don't you check his wikipedia page?
How many proofs are their for Pythagoras theorem'?
There are over 100 of them. They can be found at //www.cut-the-knot.org/pythagoras/