what is hyperbolic function?
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In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh", and the hyperbolic cosine "cosh", from which are derived the hyperbolic tangent "tanh", etc., in analogy to the derived trigonometric functions. The inverse functions are the inverse hyperbolic sine "arsinh" (also called "arсsinh" or "asinh") and so on.\n\nJust as the points (cos t, sin t) define a circle, the points (cosh t, sinh t) define the right half of the equilateral hyperbola. Hyperbolic functions are also useful because they occur in the solutions of some simple linear differential equations, notably that defining the shape of a hanging cable, the catenary.\n\nThe hyperbolic functions take a real value for real argument called a hyperbolic angle. In complex analysis, they are simply algebraic functions of exponentials, and so are entire.
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Like in pythagorean therom? Hypotenuse
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http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html\nhttp://en.wikibooks.org/wiki/Engineering_Acoustics/Bessel_Functions_and_the_Kettledrum
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Functions that maps x to x\nWhere x is an element of the function
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I know of one application in an abstruse area of physics: The sinh( ) of a scalar field occurs in gravitational theories where, for whatever reason, one emplys a metric disformally related to the 'physical' metric tensor.\n\nAlso, the shape of a freely hanging level chain is cosh( ) of displacement along the line joining ends
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If you look at a picture (aka a graph) of the function, it will all become clear...\n\nhttp://upload.wikimedia.org/wikipedia/en/3/3e/1-over-x.png
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The Blancmange function http://mathworld.wolfram.com/BlancmangeFunction.html
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For a hyperbola that opens up/down, the formula is:\n\n(y - k)^2/b^2 - (x - h)^2/a^2 = 1\nwhere:\nh,k is the center\nh, k +/- c are the foci where c^2 = a^2 + b^2\n\nSo, as given above:\nVertices are at (-4,1) and (-4,9), so the center is (-4,5). h = -4, k = 5.\nFocus is -4, 5 +/- √97, so c = √97, and therefore a^2 + b^2 = 97.\n\na^2 + b^2 = 97 can have a whole number for a and b if a and be equal 9 (9^2 = 81) and 4 (4^2 = 16) respectively. The two hyperbolae that meet your criteria then are:\n\n(y - 5)^2/9 - (x + 4)^2/4 = 1\n(y - 5)^2/4 - (x + 4)^2/9 = 1
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In complex analysis, a pole of a holomorphic function is a certain type of simple singularity that behaves like the singularity 1/z^n at z = 0. A pole of the function f(z) is a point z = a such that f(z) approaches infinity as z approaches a.\n\nZero or nothing is an important mathematical concept denoting absence which has facilitated the development of Maths and Science as we know them.\n\nA vector space is a set of vectors of the same dimensions bound by the laws and properties common to all of them
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I know u r not doing your own assignment but i cannot help it, i must answer your question.\n\nPositive curvature, elliptic\nnegative, hyperbolic
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A derivative is a function measuring the rate of change of another function. A common example is velocity. Velocity is the derivative of position, because velocity is measuring the rate of change of position. And acceleration is the derivative of velocity, because the rate of change of velocity is acceleration.\n\nIt's the basic cornerstone of calculus.
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This would most definitely be a polynomial function, since it starts with x cubed. Anything that has x cubed or higher in it, like x to the fifth power, would be a polynomial function. An equation with x squared would be a quadratic function. An equation with just x would be a linear equation.
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it is called akermen function. search web about this
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Picture a lamp close to a wall.  The lamp has a shade that is a cylinder, (shaped like a tin can with the top and bottom cut off).  The shade is parallel to the wall.  When the light is on, the shape of the light on the wall is a hyperbola.\n\nReally!
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partial differential equation (PDE) is a relation involving an unknown function of several independent variables and its partial derivatives with respect to those variables. Partial differential equations are used to formulate and solve problems that involve unknown functions of several variables, such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, elasticity, or more generally any process that is distributed in space, or distributed in space and time. Very different physical problems may have identical mathematical formulations.
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The formula\n\nAx2 + Bxy + Cy2 + Dx + Ey + F = 0\n\nis a hyperbola if 4AC < B^2.  If 4AC > B^2, then it's an ellipse.\n\n4*1*19 = 76\n13^2 = 169\n\nSo, hyperbola.
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hemidemisemiquaver\n\nhttp://en.wikipedia.org/wiki/Musical_notation