Improper Integrals What are improper integrals? An improper integral is a definite integral where one or both of the limits is either: Positive or minus infinity A point where the function is undef...
Adding and Subtracting Volumes Why might I need to add or subtract volumes of revolution? As with the area between a curve and a line or the area between 2 curves, a required volume may be created ...
Volumes of revolution around the x-axis What is a volume of revolution around the x-axis? A solid of revolution is formed when an area bounded by a function (and other boundary equations) is rotat...
Differentiating Hyperbolic Functions What are the derivatives of the hyperbolic functions? These are given in the formulae booklet You can prove them by differentiating the definitions involving e ...
Hyperbolic Identities & Equations Are there identities linking the hyperbolic functions to the circular trig functions? Yes - these can be seen using de Moivre's Theorem to write Compare these ...
Logarithmic Forms of Inverse Hyperbolic Functions What are the definitions of the inverse hyperbolic functions? Since coshx is a many-to-one function, its domain is restricted to x ≥ 0 when finding...
Hyperbolic Functions & Graphs What are the definitions of the hyperbolic functions? Hyperbolic sine This can be pronounced "shine" or "sinch" Hyperbolic cosine This can be pronounced "cosh" Hyp...
Maclaurin Series What is a Maclaurin Series? A Maclaurin series is a way of representing a function as an infinite sum of increasing integer powers of etc.) If all of the infinite number of terms ...
Method of Differences What is the Method of Differences? The Method of Differences is a way of turning longer and more complicated sums into shorter and simpler ones Sometimes when summing series, ...
