Linear Approximation

In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.

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Linear Approximation - Definition
... The linear approximation is obtained by dropping the remainder This is a good approximation for x when it is close enough to a since a curve, when closely observed ... For this reason, this process is also called the tangent line approximation ... If f is concave down in the interval between x and a, the approximation will be an overestimate (since the derivative is decreasing in that interval) ...
Comparative Statics - Linear Approximation - Stability - An Example of The Role of The Stability Assumption
... This means that the equilibrium price depends positively on the demand intercept if g – b > 0, but depends negatively on it if g – b < 0 ... Which of these possibilities is relevant? In fact, starting from an initial static equilibrium and then changing a, the new equilibrium is relevant only if the market actually goes to that new equilibrium ...