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Error Bounds

Definition

Error bounds refer to estimates used to quantify how accurate an approximation or calculation is compared to the exact value.

Analogy

Think of error bounds as a margin of error in a survey. Just like a pollster provides an estimated range within which the true value lies, error bounds give us an idea of how close our approximation is to the actual value.

Related terms

Taylor Series: Taylor series are mathematical representations that approximate functions using polynomials. They help us estimate values and understand function behavior.

Trapezoidal Rule: The trapezoidal rule is a numerical integration method that approximates the area under a curve by dividing it into trapezoids. It helps us calculate integrals when we can't find exact solutions.

Mean Value Theorem: The mean value theorem states that if a function is continuous on a closed interval and differentiable on its interior, then there exists at least one point where the derivative equals the average rate of change over that interval. It helps us analyze functions and their derivatives.