What do you mean by "compute"? Do you want to graph it? Factor it? Calculate it's function given a set of points that lie on it? If you're looking to compute the function given three points that fall on the parabola, then I have just the code for you. If you're given three points, (x1, y1), (x2, y2) and (x3, y3), then you can compute the coefficients of your quadratic equation like this: a = (y1 * (x2 - x3) + y2 * (x3 - x1) + y3 * (x1 - x2)) / (x1 * x1 * (x2 - x3) + x2 * x2 * (x3 - x1) + x3 * x3 * (x1 - x2)) b = (y1 - y2) / (x1 - x2) - a * (x1 + x2); c = y1 - (x1 * x1) * a - x1 * b; You now can calculate the y co-ordinate of any point given it's x co-ordinate by saying: y = a * x * x + b * x + c;
The derivative of a function is another function that represents the slope of the first function, slope being the limit of delta y over delta x at any two points x1,y1 and x2,y2 on the graph of the function as delta x approaches zero.
In general, it is linear if it is of the form a1x1 + a2x2 + ... + anxn + a0 = 0where a1, a2, ... an and a0 are constants, and x1, x2, ... , xn are variable.If there are only two variables then usually x1 = x and x2 = y.
Suppose you have a function y = f(x) which has an inverse. Therefore there exists a function g(y) such that g(y) = x whenever y = f(x). Now suppose a line parallel to the x axis, y = k (some constant), intersects the graph of y = f(x) at more than one point: say x1 and x2. That means that k = f(x1) and k = f(x2). Now, in the context of the function g, this means that [from the first intersection] g(k) = x1 and [from the first intersection] g(k) = x2 But the function g cannot map k to two different points. That is the contradiction which precludes the possibility of a horizontal line intersecting an invertible function more than once.
i think its pretty much the same thing because matrix X1 X2 IS ACTUALLY X1 X2
the function (x),sory I can`t use the sign of the function because it is not available. the function of (x)=4x+4 is one to one function assume function(x1)= function(x2) then 4(x1)+4 =4(x2)+4 4(x1)=4(x2) (x1)=(x2) hence,the function is one to one
x1/5
=SUM(X1:X10)
Need two points. m = slope. (X1, Y1) and (X2, Y2) m = Y2 - Y1/X2 - X1 ==============Or, if function is in this form...... Y =mX + b ======== Read off of function, or get function is this form.
x1 is single ohms. If the dial reads 40, the resistance is 40 ohms.
struct example { int fld1, fld2; } x1; printf ("fld1=%d, fld2=%d\n", x1.fld1, x1.fld2);
struct example {int fld1, fld2;};struct example x1;printf ("fld1=%d, fld2=%d\n", x1.fld1, x1.fld2);
Suppose you have a differentiable function of x, f(x) and you are seeking the root of f(x): that is, a solution to f(x) = 0.Suppose x1 is the first approximation to the root, and suppose the exact root is at x = x1+h : that is f(x1+h) = 0.Let f'(x) be the derivative of f(x) at x, then, by definition,f'(x1) = limit, as h tends to 0, of {f(x1+h) - f(x1)}/hthen, since f(x1+h) = 0, f'(x1) = -f(x1)/h [approx] or h = -f'(x1)/f(x1) [approx]and so a better estimate of the root is x2 = x1 + h = x1 - f'(x1)/f(x1).
this is the increasing function theorem, hope it helps "If F'(x) >= 0 , and all x's are and element of [a,b], Then F is increasing on [a,b]" use Mean Value Theorem (M.V.T) Let F'(x)>=0 on some interval Let x1< x2 (points from that interval) by M.V.T there is a point C which is an element of [x1,x2] such that F(x2)-F(x1) / X2- X1 = F'(C) this implies: F(x2)-F(x1) = F'(C) X [x2-x1] F'(C)>=0 [x2-x1]>0 therefore: F(x2)>=F(x1) Therefore: F is increasing on that interval.
What do you mean by "compute"? Do you want to graph it? Factor it? Calculate it's function given a set of points that lie on it? If you're looking to compute the function given three points that fall on the parabola, then I have just the code for you. If you're given three points, (x1, y1), (x2, y2) and (x3, y3), then you can compute the coefficients of your quadratic equation like this: a = (y1 * (x2 - x3) + y2 * (x3 - x1) + y3 * (x1 - x2)) / (x1 * x1 * (x2 - x3) + x2 * x2 * (x3 - x1) + x3 * x3 * (x1 - x2)) b = (y1 - y2) / (x1 - x2) - a * (x1 + x2); c = y1 - (x1 * x1) * a - x1 * b; You now can calculate the y co-ordinate of any point given it's x co-ordinate by saying: y = a * x * x + b * x + c;
y=x2+3 x1=1 x2=2 y(x1) = 1*1+3 = 4 y(x2) = 2*2+3 = 7 x2/x1 = 2, While y2/y1 = 7/4 !=2, and thus the function is nonlinear.
The formula: distance=sqrt(((x1-x2)*(x1-x2))+((y1-y2)*(y1-y2))+((z1-z2)*(z1-z2))) In DarkBASIC it's: function distance3D(x1,y1,z1,x2,y2,z2) x=x1-x2 y=y1-y2 z=z1-z2 result=sqrt((x*x)+(y*y)+(z*z)) endfunction result In classic BASIC I think it's: FUNCTION distance3D(x1,y1,z1,x2,y2,z2) x=x1-x2 y=y1-y2 z=z1-z2 result=SQRT((x*x)+(y*y)+(z*z)) RETURN result END FUNCTION