搜尋結果
Only 4 billion A shares were floated during the IPO, another 158 billion A shares were still held by China National Petroleum Corporation. 21.9 billion H shares were already floated on the Hong Kong Stock Exchange. [31] However, market capitalization based on H shares never reached $500 billion.
American retail corporation Walmart has been the world's largest company by revenue since 2014. [1] The list is limited to the largest 50 companies, all of which have annual revenues exceeding US$130 billion. This list is incomplete, as not all companies disclose their information to the media and/or general public. [3]
Wikipedia is written by volunteer editors and hosted by the Wikimedia Foundation, a non-profit organization that also hosts a range of other volunteer projects : Commons. Free media repository. MediaWiki. Wiki software development. Meta-Wiki. Wikimedia project coordination. Wikibooks.
- 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 ...
Tencent Holdings Ltd. (Chinese: 腾讯; pinyin: Téngxùn) is a Chinese multinational technology conglomerate and holding company headquartered in Shenzhen. It is one of the highest grossing multimedia companies in the world based on revenue. It is also the world's largest company in the video game industry based on its equity investments ...
The capybara[a] or greater capybara (Hydrochoerus hydrochaeris) is a giant cavy rodent native to South America. It is the largest living rodent[2] and a member of the genus Hydrochoerus. The only other extant member is the lesser capybara (Hydrochoerus isthmius). Its close relatives include guinea pigs and rock cavies, and it is more distantly ...
Google is also the largest search engine, mapping and navigation application, email provider, office suite, online video platform, photo and cloud storage provider, mobile operating system, web browser, machine learning framework, and AI virtual assistant provider in the world as measured by market share. [18]
