Linear approximation uses the tangent line at a point 'a' to estimate the function's value at a nearby point 'x'. It assumes the function is locally linear.
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Pro Tips
Closeness: The approximation is only accurate when x is close to a.
Concavity: If the function curves away significantly (high second derivative), the error increases.
Differentials: dy ≈ f'(x)dx describes the change in y.
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Fun Facts
"This method is the basis for Euler's method in solving differential equations."
"Engineers use linearization to simplify complex non-linear systems for control theory."
