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Proofs
Proof means sufficient evidence to establish the truth of something. It is obtained from deductive reasoning, rather than from empirical arguments. Proof must show that a statement is true in all cases, without a single exception.
1,294 Questions
Differentiation Rules and examples and explanation?
Differentiating is the act of finding the derivative of a function, thus allowing you to find out how the function changes as its input changes, such as finding the rate of change of the gradient of the function, and when differentiating with respect to time can allow you to give equations explaining the motion of various objects, depending on how you differentiate the functions. There are two main types of differentiation, ordinary differentiation and partial differentiation, the rules outlined below are for ordinary differentiation. While the rules for partial differentiation are not that dissimilar, they do not need to be known outside of university level mathematics and physics.
(using f' and g' to denote the derivative of the functions f and g of x respectively, x is a variable, o indicates a composite function, all other letters are constants, rules in bold are important)
Elementary rulesf = xn, f' = nx(n-1) elementary power rule
f = a, f' = 0 constant rule
f = ax, f' = a derivative of a linear function is a constant
(af +bg)' = af'+bg' linearity of differentiation, leading to the 3 following,
(af)' = af' constant multiple rule
(f+g)' = f'+g' sum rule
(f-g)' = f'-g' subtraction rule,
(fg)' = f'g + fg' product rule
(fog)' = (f(g))' = (f'(g))g' = (f'og)g' chain rule
f = 1/g, f' = -g'/g2 reciprocal rule
(f/g)' = (f'g-fg')/g2 quotient rule
f=sin(x), f'=cos(x)
f=cos(x), f'=-sin(x)
f=tan(x), f'=sec2(x)
f=sec(x), f'=sec(x)tan(x)
f=cosec(x) f'=-cosec(x)cot(x)
f=cot(x), f'=-cosec2(x)
f=exp(ax), f'=a*exp(ax)
f=exp(axn), f'=anx(n-1)*exp(axn)
f=ax, f'=(log(a))*ax
f=log(x), f'=1/x
f=log(xn), f'=nx(n-1)/xn
f=xx, f'=xx(1+log(x))
these are just the simple rules of differentiation for various functions, there are a LOT more, but they are generally only of use at university levels.
The sum is 22 times the sum of the three digits.
Yes they can be so friendly, in fact, that you could have one as your pet!!! HOW COOL WOULD THAT BE!!!! For more fox info email me on jimmyboi14@hotmail.co.uk
12 and 18
Who is the father of vedic maths?
Jagadguru Shankaracharya Shri Bharati Krishna Tirthaji Maharaja is 2the father of vedic maths
Is every statement a theorem why?
There are many kinds of statement that are not theorems:
A statement can be an axiom, that is, something that is assumed to be true without proof. It is usually self-evident, but like Euclid's parallel postulate, need not be.
A statement need not be true in all circumstances - for example, A*B = B*A (commutativity) is not necessarily true for matrix multiplication.
A statement can be false.
A statement can be self-contradictory for example, "This statement is false".
If 0 divided by 0 is equal to zero then prove that 1 equal to 2?
(2 - 1) * 0 = 0
Thus 2 - 1 = 0/0 = 0
and therefore 2 = 1
You start with one piece of paper. With each cut you increase the number of pieces by one - whether or not you cut in half. So, at the end of the process you have as many pieces as the number of cuts you made and that, in turn, depends on the rate at which you cut the paper and the time available - neither of which are given in the question.
How are the proofs of the fundamental theorem of algebra?
look in google if not there, look in wikipedia.
fundamental theorem of algebra and their proofs
Can mps equal 1 and mpc equals 0?
According to Keynes, if MPS = 1 then, in a closed system, MPC must be 0. The only alternative is to borrow - which defeats the purpose of saving all the marginal increase in income! Therefore, it is possible but most unlikely.
What other factors may play a large role in determining climate?
the presence of dark spot on sun keeps the climate in balanced state ,as these dark spots are a result some reactions radiating large amount of heat.
if no dark spots are visible ,the climate will become unstable due to less heat reaching the earth's surface-as is now in2008-10.
From 2 years the sun spots have vanished from sun and it had been a concern for the scientists all over the world.
further climate change cannot be estimated .
in 1700's during the reign of aurangzeb,the sun spots remained vanised for a long period of time and the climate in Europe decreased to such a extent that the people thought that the ice has come back.........
