If the limit exists, meaning that there is a way of choosing a value for Q ( 0 ) that makes the graph of Q a continuous function, then the function f is differentiable at a, and its derivative at a equals Q ( 0 ).

If the accused party is found guilty, the victim ( or in death, victim's family ) determines the punishment, choosing either retribution ( qisas-e-nafs ), which means execution in the case of intentional murder, and in cases of intentional battery, the amputation of the limb that was lost ; or they can choose to forgive the perpetrator.

If the match ended in a tie, one final question was played with the star of one contestant's choosing ; if the contestant can agree or disagree correctly, he / she won the match, otherwise the match went to the opponent.

If God is choosing our path for us, then what choices do we have?

The idea is that while there are composite probable primes to base a for any fixed a, we may hope there exists some fixed P < 1 such that for any given composite n, if we choose a randomly the probability that n is pseudoprime to base a is at most P. If we repeat this test k times, choosing a new a each time, the probability of n being pseudoprime to all the as tested is hence at most P < sup > k </ sup >, and as this decreases exponentially, only moderate k is required to make this probability negligibly small ( compared to, for example, the probability of computer hardware error ).

If insurance companies could perfectly observe the actions of their clients, they could deny coverage to clients choosing risky actions ( like smoking in bed or not wearing seat belts ), allowing them to provide thorough protection against risk ( fire, accidents ) without encouraging risky behavior.

He can discard his general principle in search of a better one ( for example, only obeying the Ten Commandments ), modify his general principle ( for example, choosing a different translation of the Bible, or including Jesus ' teaching from John 8: 7 " If any of you is without sin, let him be the first to cast a stone " into his understanding ), or change his opinions about the point in question to conform with his theory ( by deciding that witches really should be killed ).

If each switch is operated by a key on a typewriter, and the bulbs are labelled with letters, then such a system can be used for encryption by choosing the wiring between the keys and the bulb: for example, typing the letter < tt > A </ tt > would make the bulb labelled < tt > Q </ tt > light up.

If the tenant relies on this statement in choosing to remain in the premises, the landlord could be estopped from collecting the full rent.

" Similarly, Chen Li-an warned, " If you vote for Lee Teng-hui, you are choosing war.

If they are in the same plane, Desargues's theorem can be proved by choosing a point not in the plane, using this to lift the triangles out of the plane so that the argument above works, and then projecting back into the plane.

If no one bids, choosing instead to pass, then the dealer automatically bids 15 and play resumes as normal.

If choosing a " self-tie " bow tie, there are usually two shapes available: the " bat wing ," which is parallel-sided like a cricket bat, and the " thistle ", sometimes known as the " butterfly.

If n is the degree of P, then the splitting type is a partition Π of n. Considering also the Galois group G of K over Q, each g in G is a permutation of the roots of P in K ; in other words by choosing an ordering of α and its algebraic conjugates, G is faithfully represented as a subgroup of the symmetric group S < sub > n </ sub >.

If the game show offers $ 1, 600 behind the good door, increasing to $ 800 the expected value of choosing between doors 1 and 2, the risk premium becomes $ 300 ( i. e., $ 800 expected value minus $ 500 guaranteed amount ).

If the player's character ends up winning ( i. e. Plucky outweighing Li ' l Beeper ), the player will get an extra life, while nothing happens either if the computer wins ( i. e. Sweetie is outweighed by Shirley ) or if the round ends in a tie ( i. e. choosing Elmyra against Montana Max ).

If the team chose not to offer a contract, then the player could try to sign with a team of his choosing.

If it really stands for a deceased love, Poe's choosing to refer to Ulalume as " the thing " and " the secret " do not seem endearing terms.

If they quit before then, after choosing the career path, the Federation is less supportive to them in the Civilian world.

* If the ring is the quaternions, then choosing a subring of the quaternions isomorphic to the complex numbers makes V into an irreducible complex representation of G with Schur indicator − 1, called a quaternionic representation.

If a contestant spun a pair and a single, two questions were asked worth two points each if the contestant chose the pair or one question worth one point for choosing the single category.

* If choosing a candidate will create many new sources, its priority will rise.

If we were to reach the last round of the game, Player 2 would do better by choosing d instead of r. However, given that 2 will choose d, 1 should choose D in the second to last round, receiving 3 instead of 2.

If r ≤ c ( as in the illustration ), then choosing a central column will give a separator S with r ≤ √ n vertices, and similarly if c ≤ r then choosing a central row will give a separator with at most √ n vertices.

If the latter knows nothing about the absent sitter except his name ( given by the experimenter ), he cannot possibly give any clues, conscious or unconscious, far less ask leading questions.

If only the latter were true.

`` If asked to choose between a terrible probability and a more terrible possibility, most men will choose the latter ''.

If the latter, Amaryllis would be the correct name for the genus Hippeastrum, and a different name would have to be used for the genus discussed here.

If we are told that at least one of two statements is true ; and also told that it is not the former that is true ; we can infer that it has to be the latter that is true.

If a physical object statement is to be translatable into a sense-data statement, the former must be at least deducible from the latter.

# If the borrowed word rhymes with one or more native words, the latter tend to dictate gender.

If the latter, then Hannibal and his brothers also bore the name ' Barca '.

If the former, then justice is arbitrary ; if the latter, then morality exists on a higher order than God, who becomes little more than a passer-on of moral knowledge.

If she did the latter, then it is very possible that, after the judgment, she danced naked in front of the audience as well, accompanied by the chorus.

If the former, the stitch is denoted as a knit stitch or a plain stitch ; if the latter, as a purl stitch.

If the latter is followed, the lysogenic state is established and maintained.

#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

If readers and viewers have a priori views on the current state of affairs and are uncertain about the quality of the information about it being provided by media outlets, then the latter have an incentive to slant stories towards their customers ' prior beliefs, in order to build and keep a reputation for high-quality journalism.

If the latter subgroup cools slowly from a melt, it forms exsolution lamellae because the two components — orthoclase and albite — are unstable in solid solution.

If the latter scaling is used, an interval of proper time,, defined by

If the latter option were to win, a separate referendum would be held where Puerto Ricans would have been given the option of being admitted as a US State " on equal footing with the other states ", or becoming a " sovereign nation, either fully independent from or in free association with the United States.

If however the reverse waist lock is set from the back of the opponent, then the latter would face away from the athlete in the inverted position.

If the latter occurs, ( Alice measures 1 ) then Bob's measurement will return 0 with certainty.

If, however, a statute which did not itself contain any limitation is to be governed by another which is temporary only, the former will also be temporary and dependent upon the existence of the latter.

If an observation inductively supports the former but not the latter, then " inductively support " must refer to something other than changes in the probabilities of propositions.

If a short vowel does not precede the sound, the latter spelling is used, as in took, barge, and launch.

If the latter is the case, then as a consumer decreases consumption of one good in successive units, successively larger doses of the other good are required to keep satisfaction unchanged.

If the latter is too hard, the roots will not penetrate it readily and, as a result, the plant will be pushed up and out of the earth during the process of growth.

If we use NC reductions, that is, reductions which can operate in polylogarithmic time on a parallel computer with a polynomial number of processors, then all P-complete problems lie outside NC and so cannot be effectively parallelized, under the unproven assumption that NC ≠ P. If we use the weaker log-space reduction, this remains true, but additionally we learn that all P-complete problems lie outside L under the weaker unproven assumption that L ≠ P. In this latter case the set P-complete may be smaller.