what is a byperbolic function and what is its function in math?
449789
See for example these places:\n\nhttp://www.analyzemath.com/\n(Interesting interacctive math. graphics)\n\nhttp://mcraefamily.com/MathHelp/\nhttp://mcraeclan.com/MathHelp/GeometryHyperbolicTrigFunctions.htm
824521
this just means Y is a function of x\n\ny = x^2(2-3)\ny = -x^2
1013129
Please explain what is ~f.  I have curiosity, because neither inverse multiplicative, complex conjugate or inverse function could do that result...\n\nIt should be interesting!! Please post what is ~f !
171024
In "C", it is called the "floor" function. A quick search on wikipedia\n\nhttp://en.wikipedia.org/wiki/Floor_function\n\nshows that mathematicians favour the same terminology.
671983
A derivative is the primary mathematical tool that is used to calculate and study rates of change.\n\nf'(Xo)=lim f(x+h)-f(x) / f  (/is divide which I am sure u know)\n          \n\nK so thats really confusing-not easy trying to write out the formula on this but hope it helps a little.
448359
A convex function is a continuous function whose value at the midpoint  of every interval in its domain does not exceed the average  of its values at the ends of the interval.\n\nIn other words, a function f(x) is convex on an interval [a,b] if for any two points x_1 and x_2 in [a,b] and any  β where 0< β<1,\nf[ βx_1+(1- β)x_2)]<= βf(x_1)+(1- β)f(x_2)\n\nTake ur function and prove the above.
751599
Primarily this is an expression raised to the fifth power, and so that is the outer function:\nf(x) = x^5,  or f(u) = u^5\n\nClearly, to get your function, you  need to replace x by\nx^2 + 4x + 6, and so that is the inner function, g(x).\nChecking, note that\nf(g(x)) = f(x^2 + 4x + 6)\n           = (x^2 + 4x + 6)^5\n\nI expect you know the "chain rule" for differentiating a composite function:\ndy/dx = (dy/du)*(du/dx)\n         = 5u^4*(2x + 4) and you finish this by replacing\nu with x^2 + 4x + 6 and taking out the common factor from \n2x + 4.
785253
So are you looking for a function with a singularity on (0,1)?  That would address the question I think.\nmaybe (x-(1/2))^(1/2)\n\nTHE FIRST ANSWER IS WRONG, I THINK, BECAUSE YOUR DOMAIN IS OPEN AND DOESN'T INCLUDE 0.
1116002
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.
846806
If you want a visual answer, a function of one variable is graphed by a line, wavy or however.  A function of two variables is graphed by a surface.  Obviously, equations with two variables take more work and effort to make anything out of them, than those with just one.
337310
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.
668107
First derivatives are usually represented like this\nf_x = ( f(x+h,y) - f(x,y) )/ h\nf_y = ( f(x,y+h) - f(x,y) )/ h\n\nYour second partials should be:\n\nf_xx = ( f_x(x+h,y) - f_x(x,y)) / h\nf_yy = ( f_y(x,y+h) - f_y(x,y)) / h\n\nYour mixed partials are:\n\nf_xy = ( f_x(x,y+h) - f_x(x,y)) / h\nf_yx = ( f_y(x+h,y) - f_x(x,y)) / h\n\n\nThat is f_x is a function of x and y. To get f_xy take that functions derivative with respect to y.
825459
what is the second function?
276904
The Laplace transform *doesn't* exist for every function. For example, f(x)=exp(x^2).
363905
They are solutions to Bessell's differential equation:\n\nx^2y''+xy'+(x^2-n^2)y=0.\n\nThe solutions of this equation are called Bessell functions of order n. Using standard techniques, it is possible to find power series solutions to this equation for every n and two independent power series solutions if n is not an integer.\n\nBessell functions come up naturally from the partial differential equations of physics and have applications ranging from electromagnetism to sound. The functions are oscillatory in form, but unlike trigonometric functions, they decay towards infinity. There are books written just about these functions and their many properties.
144611
You might find this paper useful\nhttp://arxiv.org/abs/math-ph/0106027
632411
yes u mean like the turning point of a parabolic curve...yea the x-coordinate is equal to -b/2a\nor u can differentiate the equation of the curve and put it equal to zero and solve :\neg  y = ax^2 + bx + c\ndy/dx = 2ax +b \nput this equal to zero and u get x = -b/2a