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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.
The simplest way to find a limit that works in the easiest cases.
A way to simplify evaluation of limits when the limit is an indeterminate form.
How to determine the intervals where a polynomial is positive or negative.
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.
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.
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.
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?
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.
Limits at infinity