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