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...
Invariant Points What is an invariant point? When applying transformations to a shape or collection of points, there may be some points that stay in their original position; these are known as inva...
2D Transformations What is meant by a 2D geometric transformation? The following transformations can be represented (in 2D) using multiplication of a 2x2 matrix rotations (about the origin) reflect...
