Search results
Results from the WOW.Com Content Network
[6] [7] [a] The parentheses can be omitted if the input is a single numerical variable or constant, [2] as in the case of sin x = sin(x) and sin π = sin(π). [a] Traditionally this convention extends to monomials; thus, sin 3x = sin(3x) and even sin 1 / 2 xy = sin(xy/2), but sin x + y = sin(x) + y, because x + y is not a monomial ...
It follows from the preceding equations that = when x is an integer (this results from the repeated-multiplication definition of the exponentiation). If x is real, = results from the definitions given in preceding sections, by using the exponential identity if x is rational, and the continuity of the exponential function otherwise.
x 1 = x; x 2 = x 2 for i = k - 2 to 0 do if n i = 0 then x 2 = x 1 * x 2; x 1 = x 1 2 else x 1 = x 1 * x 2; x 2 = x 2 2 return x 1 The algorithm performs a fixed sequence of operations ( up to log n ): a multiplication and squaring takes place for each bit in the exponent, regardless of the bit's specific value.
This set is ordered lexicographically with the least significant position first: we write f < g if and only if there exists x ∈ β with f(x) < g(x) and f(y) = g(y) for all y ∈ β with x < y. This is a well-ordering and hence gives an ordinal number. The definition of exponentiation can also be given by transfinite recursion on the exponent β.
In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number of multiplications. Using the form of the shortest addition chain , with multiplication instead of addition, computes the desired exponent (instead of multiple) of the base .
The fx-39 was one of the first to offer order of operations, where 2+3*5 is 17 and not 25. This feature is almost universally assumed on modern scientific calculators, but this was a new feature in 1978. In contrast the fx-29 did not have operator precedence. Hyperbolic Functions. Casio introduced hyperbolic functions in the fx-39 along with ...
For instance, e x can be defined as (+). Or e x can be defined as f x (1), where f x : R → B is the solution to the differential equation df x / dt (t) = x f x (t), with initial condition f x (0) = 1; it follows that f x (t) = e tx for every t in R.
The parameters of the hyperoperation hierarchy are sometimes referred to by their analogous exponentiation term; [15] so a is the base, b is the exponent (or hyperexponent), [12] and n is the rank (or grade), [6] and moreover, (,) is read as "the bth n-ation of a", e.g. (,) is read as "the 9th tetration of 7", and (,) is read as "the 789th 123 ...