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Terms with infinitely many sine factors would necessarily be equal to zero. When only finitely many of the angles are nonzero then only finitely many of the terms on the right side are nonzero because all but finitely many sine factors vanish. Furthermore, in each term all but finitely many of the cosine factors are unity.
It is the most comprehensive, detailed and thick dictionary in the history of Urdu language. [ citation needed ] It is published by the Urdu Lughat Board, Karachi. The dictionary was edited by the honorary director general of the board Maulvi Abdul Haq who had already been working on an Urdu dictionary since the establishment of the Urdu ...
The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2x) A curve intersecting an asymptote infinitely many times In analytic geometry , an asymptote ( / ˈ æ s ɪ m p t oʊ t / ) of a curve is a line such that the distance between the curve and the line approaches zero as one or ...
All the common words, idioms, proverbs, and modern academic, literary, scientific, and technical terms of the Urdu language have been listed. Only those obsolete words and idioms have been included which are found in ancient books. They are indicated by the symbol "Qaaf". The English words that are commonly used in Urdu have also been included. [5]
A uniformly recurrent word is a recurrent word in which for any given factor X in the sequence, there is some length n X (often much longer than the length of X) such that X appears in every block of length n X. [1] [6] [7] The terms minimal sequence [8] and almost periodic sequence (Muchnik, Semenov, Ushakov 2003) are also used.
Euler's formula states that, for any real number x, one has = + , where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted cis x ("cosine plus i sine").
Urdu in its less formalised register is known as rekhta (ریختہ, rek̤h̤tah, 'rough mixture', Urdu pronunciation:); the more formal register is sometimes referred to as زبانِ اُردُوئے معلّٰى, zabān-i Urdū-yi muʿallá, 'language of the exalted camp' (Urdu pronunciation: [zəbaːn eː ʊrdu eː moəllaː]) or لشکری ...
For example, in mathematics, "or" means "one, the other or both", while, in common language, it is either ambiguous or means "one or the other but not both" (in mathematics, the latter is called "exclusive or"). Finally, many mathematical terms are common words that are used with a completely different meaning. [100]