###### Answer: A. The leading coefficients of f(x) and g(x) are opposites.

The statement ” f ( x ) is O( g ( x ))” as defined above is usually written as f ( x ) = O( g ( x )). Some consider this to be an abuse of notation since the use of the equals sign could be misleading as it suggests a symmetry that this statement does not have. As de Bruijn says O( x ) = O( x 2) is true but O( x 2) = O( x …

Graph of f ( x ) = e x (blue) with its quadratic approximation P 2 ( x ) = 1 + x + x 2 /2 (red) at a = 0. Note the improvement in the approximation. Note the improvement in the approximation. For a better approximation to f ( x ) we can fit a quadratic polynomial instead of a linear function:

Surjective function – Wikipedia

Quadratic function – Wikipedia

Surjective function – Wikipedia

For example a univariate (single-variable) quadratic function has the form = + + ≠in the single variable x . The graph of a univariate quadratic function is a parabola whose axis of symmetry is parallel to the y-axis as shown at right.. If the quadratic function is set equal to zero then the result is a quadratic equation.The solutions to the univariate equation are called the roots of the …

A function f : X → Y is surjective if and only if it is right-cancellative: given any functions g h : Y → Z whenever g o f = h o f then g = h. This property is formulated in terms of functions and their composition and can be generalized to the more general notion …

In numerical analysis Newton’s method also known as the Newton–Raphson method named after Isaac Newton and Joseph Raphson is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued fun…