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  1. Marty Stratton and Hugo Martin, directors of Doom. Doom is a first-person shooter video game and a reboot of the Doom franchise released on May 13, 2016. Players take the role of an unnamed space marine who battles demonic forces within an energy-mining facility on Mars and in Hell. The game also has an online multiplayer mode and a level editor.

  2. Current ISO 3166 country codes. The sortable table below contains the three sets of ISO 3166-1 country codes for each of its 249 countries, links to the ISO 3166-2 country subdivision codes, and the Internet country code top-level domains (ccTLD) which are based on the ISO 3166-1 alpha-2 standard with the few exceptions noted.

  3. en.wikipedia.org › wiki › WikipediaWikipedia - Wikipedia

    Wikipedia[note 3] is a free content online encyclopedia written and maintained by a community of volunteers, known as Wikipedians, through open collaboration and the use of the wiki-based editing system MediaWiki. Wikipedia is the largest and most-read reference work in history.[3][4] It is consistently ranked as one of the ten most popular ...

  4. t. e. The Belt and Road Initiative ( BRI or B&R [1] ), known in China as the One Belt One Road [a] and sometimes referred to as the New Silk Road, [2] is a global infrastructure development strategy adopted by the Chinese government in 2013 to invest in more than 150 countries and international organizations. [3]

    • Characterizing Properties
    • Useful Relations
    • Second Derivatives
    • Standard Integrals
    • Taylor Series Expressions
    • Infinite Products and Continued Fractions
    • Comparison with Circular Functions
    • Relationship to The Exponential Function
    • Hyperbolic Functions For Complex Numbers
    • See Also

    Hyperbolic cosine

    It can be shown that the area under the curve of the hyperbolic cosine (over a finite interval) is always equal to the arc lengthcorresponding to that interval:

    Hyperbolic tangent

    The hyperbolic tangent is the (unique) solution to the differential equation f ′ = 1 − f 2, with f (0) = 0.

    The hyperbolic functions satisfy many identities, all of them similar in form to the trigonometric identities. In fact, Osborn's rule states that one can convert any trigonometric identity (up to but not including sinhs or implied sinhs of 4th degree) for θ {\displaystyle \theta } , 2 θ {\displaystyle 2\theta } , 3 θ {\displaystyle 3\theta } or θ {...

    Each of the functions sinh and cosh is equal to its second derivative, that is: All functions with this property are linear combinations of sinh and cosh, in particular the exponential functions e x {\displaystyle e^{x}} and e − x {\displaystyle e^{-x}} .

    The following integrals can be proved using hyperbolic substitution: where C is the constant of integration.

    It is possible to express explicitly the Taylor series at zero (or the Laurent series, if the function is not defined at zero) of the above functions. The sum of the sinh and cosh series is the infinite series expression of the exponential function. The following series are followed by a description of a subset of their domain of convergence, where...

    The following expansions are valid in the whole complex plane: 1. sinh ⁡ x = x ∏ n = 1 ∞ ( 1 + x 2 n 2 π 2 ) = x 1 − x 2 2 ⋅ 3 + x 2 − 2 ⋅ 3 x 2 4 ⋅ 5 + x 2 − 4 ⋅ 5 x 2 6 ⋅ 7 + x 2 − ⋱ {\displaystyle \sinh x=x\prod _{n=1}^{\infty }\left(1+{\frac {x^{2}}{n^{2}\pi ^{2}}}\right)={\cfrac {x}{1-{\cfrac {x^{2}}{2\cdot 3+x^{2}-{\cfrac {2\cdot 3x^{2}}{4\cd...

    The hyperbolic functions represent an expansion of trigonometry beyond the circular functions. Both types depend on an argument, either circular angle or hyperbolic angle. Since the area of a circular sector with radius r and angle u (in radians) is r2u/2, it will be equal to u when r = √2. In the diagram, such a circle is tangent to the hyperbola ...

    The decomposition of the exponential function in its even and odd partsgives the identities Additionally,

    Since the exponential function can be defined for any complex argument, we can also extend the definitions of the hyperbolic functions to complex arguments. The functions sinh z and cosh z are then holomorphic. Relationships to ordinary trigonometric functions are given by Euler's formulafor complex numbers: Thus, hyperbolic functions are periodic ...

  5. en.wikipedia.org › wiki › PhilippinesPhilippines - Wikipedia

    It is the world's twelfth-most-populous country, with diverse ethnicities and cultures. Manila is the country's capital, and its most populated city is Quezon City. Both are within Metro Manila . Negritos, the archipelago's earliest inhabitants, were followed by waves of Austronesian peoples.

  6. en.wikipedia.org › wiki › 00 - Wikipedia

    0 (zero) is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 has the result 0, and consequently, division ...

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