Pages similar to: Limits at infinity Limits of exponential functions at infinity Calculating limits of exponential functions as a variable goes to infinity. Limits with cancellation Calculating limits of a fraction my canceling factors from the numerator and denominator. Domain of functions How to determine the domain of a function. Lines (and other items in Analytic Geometry) How to describe the equation for a line in terms of horizontal and vertical coordinates. Elementary limits The simplest way to find a limit that works in the easiest cases. L'Hospital's rule A way to simplify evaluation of limits when the limit is an indeterminate form. Polynomial inequalities How to determine the intervals where a polynomial is positive or negative. Trigonometric integrals Using trigonometric identities to calculate integrals involving trigonometric functions. Linear approximations: approximation by differentials Approximating the value of a function near a point by its tangent line formula. Implicit differentiation Differenting a function that is defined implicitly in terms of a relation between two variables. Exponential growth and decay: a differential equation Solving a differential equation to find an unknown exponential function. Area and definite integrals Integrating to find the area under a curve or the area between two curves. Intermediate Value Theorem, location of roots Using the Intermediate Value Theorem to find small intervals where a function must have a root. Trigonometric substitution Using trigonometric substitution to simplify integrals involving square roots. A refresher on the chain rule How to compute the derivative of a composition of functions. Partial fractions Using algebra to simplify the integral of rational functions. 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? Newton's Method A method to approximate the roots to an equation. Graphing rational functions, asymptotes Finding vertical and horizontal asymptotes of functions to aid in graphing them. Determining tolerance/error in Taylor polynomials. Calculating with what tolerance a Taylor polynomial approximates a function on an interval.