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Pages similar to: Taylor polynomials: formulas

• 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.
• Prototypes: More serious questions about Taylor polynomials
  Questions regarding using Taylor polynomials to approximate a function over an interval.
• 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?
• Integrating Taylor polynomials: first example
  An example showing how to integrate a Taylor polynomial and interpret the result.
• 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.
• Introduction to Taylor's theorem for multivariable functions
  Development of Taylor's polynomial for functions of many variables.
• Multivariable Taylor polynomial example
  Example of a calculating a second-degree multivariable Taylor polynomial.
• The idea of the derivative of a function
  The derivative of a function as the slope of the tangent line.
• Derivatives of polynomials
  How to compute the derivative of a polynomial.
• Derivatives of more general power functions
  How to compute the derivative of power functions.
• A refresher on the quotient rule
  How to compute the derivative of a quotient.
• A refresher on the product rule
  How to compute the derivative of a product.
• A refresher on the chain rule
  How to compute the derivative of a composition of functions.
• Related rates
  Calculating one derivative in terms of another derivative.
• Intermediate Value Theorem, location of roots
  Using the Intermediate Value Theorem to find small intervals where a function must have a root.
• Derivatives of transcendental functions
  A list of formulas for taking derivatives of exponential, logarithm, trigonometric, and inverse trigonometric functions.
• L'Hospital's rule
  A way to simplify evaluation of limits when the limit is an indeterminate form.

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