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, ...
Sums of Integers, Squares & Cubes How can we use sigma notation? When writing the sum of a series you can use sigma notation The series can instead be written as This means “the sum of all the...
Linear Transformations of Roots What is a Linear Transformation? A linear transformation can be expressed as where: w is the new root x is the original root p and q are constants If you perform a ...
Roots of Quadratics How are the roots of a quadratic linked to its coefficients? Because a quadratic equation (where ) has roots and , you can write this equation instead in the form Note that It...
