Linear approximation and differentials from "summary" of Differential Calculus by S Balachandra Rao
Linear approximation and differentials are powerful tools in the study of calculus. They allow us to approximate the value of a function at a certain point by using the tangent line to that function at that point. This tangent line serves as an approximation to the function near the point of interest. To understand linear approximation better, let's consider a function f(x) and a point x=a. The tangent line to f(x) at x=a is given by the equation of the form y=f(a)+f'(a)(x-a). Here, f'(a) represents the derivative of the function f(x) evaluated at x=a. This equation represents the linear approximation to the...
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