###### Answer: C. 6(3) – 4 + 32

Wed Nov 10 2004 13:30:00 GMT-0500 (Eastern Standard Time) · Then f ( x ) g ( x ) = 4x 2 + 4x + 1 = 1. Thus deg( f ⋅ g ) = 0 which is not greater than the degrees of f and g (which each had degree 1). Since the norm function is not defined for the zero element of the ring we consider the degree of the polynomial f ( x ) = 0 to also be undefined so that it follows the rules of a norm in a Euclidean domain.

Omitting this factor results in the simplified form x 4 . Thus we say that f ( x ) is a “big O” of x 4 . Mathematically we can write f ( x ) = O( x 4 ). One may confirm this calculation using the formal definition: let f ( x ) = 6x 4 − 2x 3 5 and g ( x ) = x 4 . Applying the formal definition from above the statement that f ( x ) = O( x 4 ) is equivalent to …

The Stolz–Cesàro theorem is a similar result involving limits of sequences but it uses finite difference operators rather than derivatives.. Geometric interpretation. Consider the curve in the plane whose x -coordinate is given by g (t) and whose y-coordinate is given by f (t) with both functions continuous i.e. the locus of points of the form [ g (t) f (t)].

More formally f = g if f ( x ) = g ( x ) for all x ∈ X where f : X → Y and g : X → Y. [8] [9] [note 4 ] The domain and codomain are not always explicitly given when a function is defined and without some (possibly difficult) computation one might only know that the domain is contained in a larger set.

Not every undefined algebraic expression corresponds to an indeterminate form. For example the expression / is undefined as a real number but does not correspond to an indeterminate form because any limit that gives rise to this form will diverge to infinity if the denominator gets closer to 0 but never be 0.. A expression that arises by ways other than applying the algebraic …