So its limit as x goes to a exists and equals Q ( g ( a )), which is f ′( g ( a )).

So any point P =( x, y ) on the parabola will be equidistant both to ( 0, f ) and ( x ,- f ).

So, the parabola can be written as ; and for a parabola such as f ( x )= x², the a coefficient is 1, so the focus F is ( 0, ¼ )

So, just like one can find the value of an Integral ( f = dF ) over a 1-dimensional manifolds () by considering the anti-derivative ( F ) at the 0-dimensional boundaries (), one can generalize the fundamental theorem of calculus, with a few additional caveats, to deal with the value of integrals ( dω ) over n-dimensional manifolds ( Ω ) by considering the anti-derivative ( ω ) at the ( n-1 )- dimensional boundaries ( dΩ ) of the manifold.

So any multiple of g ( x, y )- 3 may be added to f ( x, y ) leaving f ( x, y ) unchanged in the region of interest ( above the circle where our original constraint is satisfied ).

So in this example many just write f ( x )=

So that the right-hand side of equation () is unaffected by changing the basis f to any other basis fA whatsoever.

So if f is a real valued function on M, then

So, f is constant.

So if α in C < sub > n </ sub >( X ) is an n-cycle, then f < sub >#</ sub >( α ) and g < sub >#</ sub >( α ) differ by a boundary:

The construction requires that each computation step in M ' corresponds to at least 2 computation steps of M. So M ' takes no more than f ( n )/ 2 steps, after an initial linear number of steps to convert the input tape into the compressed representation.

So Price Function ( P ) = f ( s1, s2, s3 ... sj ; n1, n2, n3 ,... nj ; e1, e2, e3 ,... ej )

So why not substitute the value f ( a ) for f itself?

So there must exist a polynomial g with ( infinity ) norm 1 / 90 such that f + g has ( at least ) a root on the unit circle.

So, redefining f to be 0 on this open set if necessary, we may assume that f is bounded and hence integrable.

So any store with low sales and high shrink were closed before the sale, along with most stores that were in the same mall as existing f. y. e.

So great a man could not but understand, too, that the thing that moves men to sacrifice their lives is not the error of their thought, which their opponents see and attack, but the truth which the latter do not see -- any more than they see the error which mars the truth they themselves defend.

So we see that a specialist is a man who knows more and more about less and less as he develops, as contrasted to the generalist, who knows less and less about more and more.

So in these pages the term `` technology '' is used to include any and all means which could amplify, project, or augment man's control over himself and over other men.

So it is that we relive his opening statement in the first television address with the dramatic immediacy of the present.

So far as the existing body of formal principle and procedure is concerned, categorical novelties are not to be anticipated in Jewish-Gentile relationships ; ;

Again omitting recent developments, E.T. Leeds' dictum of 1913 has stood unchallenged: `` So far as archaeology is concerned, there is not the least warrant for the second ( shore occupied by ) of these theories ''.

So far as I am concerned, the child is unmistakably father to the man, despite the obvious fact that child and father differ greatly -- sometimes for the better and sometimes for the worse.

So far as the record is concerned, the Western powers have not acquiesced and should not do so.

So, while we properly inveigh against the new poisoning, history is not likely to justify the pose of righteousness which some in the West were so quick to assume when Mr. Khrushchev made his cynical and irresponsible threat.

So don't see yourself as a heroine or fancy this little adventure is an event of major importance ''.

( Note: So far as State Police cars are concerned, only their replacement is under this division ).

So many times I have wondered why veterinarians do not wipe the table clean before each new canine patient is placed on it for examination.

So far as I can see, there is only one way out for the positivist.

So far these remarks, like most criticisms of Hardy, have tacitly assumed that his poetry is all of a piece, one solid mass of verse expressing a sensibility at a single stage of development.

So it is with Great Expectations, whether the hands be Orlick's as he strikes down Mrs. Gargery or Pip's as he steals a pie from her pantry.

So Dartmouth is moving closer to the others in the Ivy group.

So, too, is the mathematical competence of a college graduate who has majored in mathematics.

So is the time of the novel.

`` So there it is '', he said.

So what I am trying to tell you is the ' why ' -- that is my point -- and that concerns the spirit of the matter.

So you can see that Gerald G. Ramsey, director of SMU's food services, is not the ordinary type of craven, women-trodden chef.

So it is too with many other spirits which we all know: the spirit of Nazism or Communism, school spirit, the spirit of a street corner gang or a football team, the spirit of Rotary or the Ku Klux Klan.

The biblical symbol for this affirmation is expressed in the words: `` So God created man in his own image ; ;

In So Long And Thanks For All The Fish, Arthur Dent purchases a computer for the purpose of star mapping ; Adams makes only one disparaging comment about this decision.

Most often it is used in the context of a manifold M. The mapping class group of M is interpreted as the group of isotopy-classes of automorphisms of M. So if M is a topological manifold, the mapping class group is the group of isotopy-classes of homeomorphisms of M. If M is a smooth manifold, the mapping class group is the group of isotopy-classes of diffeomorphisms of M. Whenever the group of automorphisms of an object X has a natural topology, the mapping class group of X is defined as Aut ( X )/ Aut < sub > 0 </ sub >( X ) where Aut < sub > 0 </ sub >( X ) is the path-component of the identity in Aut ( X ).

In 1996, Computer Gaming World ranked it as the 83rd best game of all time, stating: " So good that a rival publisher tried to steal it, this cyberpunk game used rotoscoping, hot spot mapping, and cinematic cuts long before they were standard ," as well as the 12th most innovative computer game for pioneering of " using a dynamic, hot-spotted map as the game world travel interface.

So, projection onto the first coordinate is a continuous, and invertible, mapping from the upper semicircle to the open interval (− 1, 1 ):