Pages similar to: Historical and theoretical comments: Mean Value Theorem Taylor polynomials: formulas Different ways of writing Taylor's formula with remainder term. Determining tolerance/error in Taylor polynomials. Calculating with what tolerance a Taylor polynomial approximates a function on an interval. How large an interval with given tolerance for a Taylor polynomial? Given a Taylor polynomial expanded around a point, on how large an interval around the point does it achieve a required tolerance? Achieving desired tolerance of a Taylor polynomial on desired interval For a given interval around a point, how many terms of a Taylor polynomial expanded around that point must be used to achieve a required tolerance? Classic examples of Taylor polynomials Some of the most famous (and important) examples of Taylor expansions. Computational tricks regarding Taylor polynomials A short cut to calculating Taylor polynomials in terms of Taylor polynomials of simple functions. Integrating Taylor polynomials: first example An example showing how to integrate a Taylor polynomial and interpret the result. Prototypes: More serious questions about Taylor polynomials Questions regarding using Taylor polynomials to approximate a function over an interval. Integrating the error term of a Taylor polynomial: example An example showing how to integrate the error term of Taylor polynomial and interpret the result. Linear approximations: approximation by differentials Approximating the value of a function near a point by its tangent line formula. Trigonometric integrals Using trigonometric identities to calculate integrals involving trigonometric functions. Intermediate Value Theorem, location of roots Using the Intermediate Value Theorem to find small intervals where a function must have a root. A refresher on the chain rule How to compute the derivative of a composition of functions. Exponential growth and decay: a differential equation Solving a differential equation to find an unknown exponential function. Implicit differentiation Differenting a function that is defined implicitly in terms of a relation between two variables. Approximating functions by quadratic polynomials Determining how to use information from the second derivative to form a quadratic approximation to a function. Area and definite integrals Integrating to find the area under a curve or the area between two curves. Minimization and maximization refresher How to calculate the maxima and minima of a differentiable function. An algebra trick for finding critical points An old algebraic trick that can make finding critical points much easier. Related rates Calculating one derivative in terms of another derivative.