When g ( x ) equals g ( a ), then the difference quotient for is zero because f ( g ( x )) equals f ( g ( a )), and the above product is zero because it equals f ′( g ( a )) times zero.

When intelligence quotient ( IQ ) tests are initially standardized using a sample of test-takers, by convention the average of the test results is set to 100 and their standard deviation is set to 15 or 16 IQ points.

When intelligence quotient ( IQ ) tests are initially standardized using a sample of test-takers, by convention the average of the test results is set to 100 and their standard deviation is set to 15 IQ points.

When K is the real numbers, some of the p < sub > i </ sub > might be quadratic, so in the partial fraction decomposition a quotient of a linear polynomial by a power of a quadratic will occur.

# When dividing two numbers, for example, n divided by m, n is the dividend and m is the divisor ; the answer is the quotient.

When the less complicated number ring is taken to be the ring of integers, Z, then the norm of a nonzero ideal I of a number ring R is simply the size of the finite quotient ring R / I.

When a and d are real numbers, with d non-zero, a can be divided by d without remainder, with the quotient being another real number.

When defining quotients of schemes by group actions, it is often impossible for the quotient to be a scheme and still satisfy desirable properties for a quotient.

When V is an inner product space, the quotient V / ker ( L ) can be identified with the orthogonal complement in V of ker ( L ).

When Γ is isomorphic to the fundamental group of a hyperbolic 3-manifold, then the quotient space H < sup > 3 </ sup >/ Γ becomes a Kleinian model of the manifold.

When a mixture of A and B is made up and the reaction is allowed to occur, the reaction quotient, Q < sub > r </ sub >, is defined as:

When it first debuted with the format, its slogan was " Music For The Diva In You ", a reference to the female audience it targeted and the high quotient of female artists on its playlist.

When Heidegger and Sartre speak of a contrast between being and existence, they may be right, I don't know, but their language is too philosophical for me.

When they express themselves it is incandescent hatred that shines forth, the rage of repudiation, the ecstasy of negation.

When I try to work out my reasons for feeling that this passage is of critical significance, I come up with the following ideas, which I shall express very briefly here and revert to in a later essay.

When the proprietor dies, the establishment should become a corporation until it is either acquired by another proprietor or the government decides to drop it.

When the reactionary response is thus bolstered by an intellectual defense, the characteristics of that defense are explicable only in terms of the basic attitudes of unanalyzed reaction.

When I take over Taliesin, the first thing I'll do is fire you ''.

When someone in the audience rose and asked how does it feel to be a celebrity, Carl said, `` A celebrity is a fellow who eats celery with celerity ''.

When decision makers act within this frame they determine whether a claim put forward in the name of religion is to be accepted by the larger community as appropriate to religion.

When we consider the disorganized state of the world community, and the legacy of predispositions adversely directed against all who are identified as Jews, it is obvious that the struggle for the minds and muscles of men needs to be prosecuted with increasing vigor and skill.

When we turn to Aristotle's ideas on the moral measure of literature, it is at once apparent that he is at times equally concerned about the influence of the art.

When their faith in civil liberties is tested against strong pressures of social expediency in specific issues, e.g., suppression of `` dangerous ideas '', many waver and give in.

There is, of course, nothing new about dystopias, for they belong to a literary tradition which, including also the closely related satiric utopias, stretches from at least as far back as the eighteenth century and Swift's Gulliver's Travels to the twentieth century and Zamiatin's We, Capek's War With The Newts, Huxley's Brave New World, E. M. Forster's `` The Machine Stops '', C. S. Lewis's That Hideous Strength, and Orwell's Nineteen Eighty-Four, and which in science fiction is represented before the present deluge as early as Wells's trilogy, The Time Machine, `` A Story Of The Days To Come '', and When The Sleeper Wakes, and as recently as Jack Williamson's `` With Folded Hands '' ( 1947 ), the classic story of men replaced by their own robots.

When I first came across Samuel Johnson's pronouncement, `` the remedy for the ills of life is palliative rather than radical '', it seemed to me to sum up the profoundest of political and social truths.

When all else fails, it is argued that open sessions slow down governmental operations.

When a person has thoughtlessly or deliberately caused us pain or hardship it is not always easy to say, `` Just forget it ''.

When a person meets God's requirements for the experience of forgiveness he is forgiven.

When I hold my son he stiffens his whole body in my arms until he is as straight and stiff as a board.

When different colors are used, she is just as likely to color trees purple, hair green, etc..

When we become firm enough to stand for those ideals which we know to be right, when we become hard enough to refuse to aid nations which do not permit self-determination, when we become strong enough to resist any more drifts towards socialism in our own Nation, when we recognize that our enemy is Communism not war, and when we realize that concessions to Communists do not insure peace or freedom, then, and only then will we no longer be `` soft ''.

When one powerful nation strives to emulate the success of another, it is only natural.

When a man is laid to rest, he is entitled to stay put.

When I talked to Ching about it, he said, Everyone can learn, if he is not a Reactionary or lazy.

When data objects are stored in an array, individual objects are selected by an index that is usually a non-negative scalar integer.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

When α is an integer, moreover, as was similarly the case for the functions of the first kind, the following relationship is valid:

When α is an integer, the Bessel functions J are entire functions of x.

When the numbers are very large, no efficient, non-quantum integer factorization algorithm is known ; an effort concluded in 2009 by several researchers factored a 232-digit number ( RSA-768 ), utilizing hundreds of machines over a span of 2 years.

When discussing what complexity classes the integer factorization problem falls into, it's necessary to distinguish two slightly different versions of the problem:

This set, consisting of the integers congruent to a modulo n, is called the congruence class or residue class or simply residue of the integer a, modulo n. When the modulus n is known from the context, that residue may also be denoted.

When the function's argument is 0 ( zero ) it will return the integer 1 ( one ).

When m is chosen so that ( a + bm )/ k is an integer, so are the other two numbers in the triple.

When the oscillator is long and thin, such as a guitar string, or the column of air in a trumpet, many of the partials are integer multiples of the fundamental frequency ; these are called harmonics.

# When the balanced equation for a reaction is multiplied by an integer, the corresponding value of ΔH must be multiplied by that integer as well.

When originally developed, for the Intel i860, the use of integer math made sense ( both 2D and 3D calculations required it ), but as graphics cards that did much of this became common, integer SIMD in the CPU became somewhat redundant for graphical applications.

The derivation of de Moivre's formula above involves a complex number to the power n. When the power is not an integer, the result is multiple-valued, for example, when n = ½ then:

Exponentiation is a mathematical operation, written as b < sup > n </ sup >, involving two numbers, the base b and the exponent ( or index or power ) n. When n is a positive integer, exponentiation corresponds to repeated multiplication ; in other words, a product of n factors, each of which is equal to b ( the product itself can also be called power ):

When n is an integer, the solution P < sub > n </ sub >( x ) that is regular at x = 1 is also regular at x = − 1, and the series for this solution terminates ( i. e. is a polynomial ).

When,, denote integer numbers, it can be shown that.

When is a non-negative integer, then gives the number of

When spoken about graph labeling with unique labels, commonly taken from the integer range 1 ,..., n, where n is the number of the vertices of the graph, two labeled graphs are said to be isomorphic if the corresponding underlying unlabeled graphs are isomorphic.

When we want to write functions to make an abstract data type, we wish to write functions to interface with the data type, and thus we want to extract some data from the data type, for example, just the string or just the integer part of.

When a string is bowed or tone in a wind instrument initiated by vibrating reed or lips, a phenomenon called mode-locking counteracts the natural inharmonicity of the string or air column and causes the overtones to lock precisely onto integer multiples of the fundamental pitch, even though these are slightly different than the natural resonance points of the instrument.

When a man proves a positive integer to exist, he should show how to find it.

When the overtones are integer multiples ( e. g., 2 ×, 3 × ... 6 × ... ) of the fundamental frequency ( called harmonics ), then the oscillation is periodic, i. e., it vibrates in exactly the same way over and over again.