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The general equation for a linear approximation is f(x) ≈ f(x0) + f'(x0)(x-x0) where f(x0) is the value of the function at x0 and f'(x0) is the derivative at x0. This describes a tangent line used to approximate the function.

In higher order functions, the same concept can be applied. f(x,y) ≈ f(x0,y0) + fx(x0,y0)(x-x0) + fy(x0,y0)(y-y0) where f(x0,y0) is the value of the function at (x0,y0), fx(x0,y0) is the partial derivative with respect to x at (x0,y0), and fy(x0,y0) is the partial derivative with respect to y at (x0,y0). This describes a tangent plane used to approximate a surface.

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โˆ™ 2008-11-01 03:43:07
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Q: Equation for linear approximation
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How can you tell if a linear appoximation is too large or too small?

The precision of a linear approximation is dependent on the concavity of the function. If the function is concave down then the linear approximation will lay above the curve, so it will be an over-approximation ("too large"). If the function is concave up then the linear approximation will lay below the curve, so it will be an under-approximation ("too small").

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No a linear equation are not the same as a linear function. The linear function is written as Ax+By=C. The linear equation is f{x}=m+b.

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The linear system is a math model of a system that is based on the use of a linear operator. The linear system and functional approximation to solve the equation Ax equals b for x by calculating an LU decomposition of A back solving where A equals 2 1 1 and b equals 2 11 cannot be solved, because it is missing more information.

How do you figure out if an equation is a linear equation?

An equation is linear if the highest power of the unknown in the equation is 1for example an equation with just a variable to the power one such as x, y and so on is linear but one with x2, y2 and above is not linear

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A linear equation can have only one zero and that is the value of the variable for which the equation is true.

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A linear equation has no higher powers than 1. This is linear.

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Y = 5X - 3It form a linear function; a line.

How can the degree of the equation tell us if the equation is linear or not?

A linear equation always has a degree of one because the slope has to be constant to form a line. So, x + 7 is linear, 7 - x is linear, 4x - 3.7 is linear, but anything with x2 , etc. is not linear.

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linear (A+)

Why Do you Study linear equations?

we study linear equation in other to know more about quadratic equation

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Because that is how a linear equation is defined!

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aX+bY+cZ=0 Is a type of linear equation.

Where did the word linear equation came from?

It is an equation which, if plotted will be represented by a straight line (hence linear).

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a linear equation

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When it is a linear equation.

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It is a linear equation.

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A linear equation is when each term in the algebraic equation is either a constant or the product has a single variable and a constant.

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a linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable.

Definition of linear equations?

A linear equation an equation whose graph is a line. A linear equation is made up of two expressions set equal to each other.

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what is anther name for the y term in a linear equation

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y = 2x + 1 IS a linear equation!

Is y equals 5x2 plus 2 a linear equation?

Assuming that the 2 in "5x2" is a power (5x2), then no, this is not a linear equation. It is a parabolic equation.

What is the y-intercept of a linear equation?

The y-intercept of a linear equation is the point where the graph of the line represented by that equation crosses the y-axis.