Ví dụ về việc sử dụng Odd function trong Tiếng anh và bản dịch của chúng sang Tiếng việt
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Odd functions.
The others are odd functions.
Thus it is an odd function, that is,- sinh x= sinh(- x), and sinh 0= 0.
Put another way, H- 1/2 is then an odd function.
The product of two odd functions is an even function. .
The sine function and all of its Taylor polynomials are odd functions.
The Fourier series of a periodic odd function includes only sine terms.
Even functions and on the right-hand side over here, we will talk about odd functions.
The Maclaurin series of an odd function includes only odd powers.
However, the odd functions do not form an algebra over the reals, as they are not closed under multiplication.
The product of an even function and an odd function is an odd function.
The real part of f{\displaystyle f} is an even function, the imaginary part of f{\displaystyle f}is an odd function.
The quotient of an even function and an odd function is an odd function.
The integral of an odd function from- A to+A is zero(where A is finite, and the function has no vertical asymptotes between- A and A).
In some cases, you may want to use the EVEN and the ODD functions to round up to the nearest even or odd number.
For an odd function that is integrable over a symmetric interval, e.g.[- A, A]{\displaystyle[-A, A]}, the result of the integral over that interval is zero; that is[2].
Then we can construct another odd function h: S n→ S n- 1{\displaystyle h: S^{n}\to S^{n-1}} by.
The quotient of two even functions isan even function. The quotient of two odd functions is an even function. .
You may want to use the EVEN and the ODD functions to round up to the nearest even or odd number.
They are named for the parity of the powers of the power functions which satisfy each condition: the function f( x)= x n{\displaystyle f( x)= x^{ n}} is an even function if n is an even integer,and it is an odd function if n is an odd integer.
Proof: If the theorem is correct, then every continuous odd function from S n{\displaystyle S^{n}} must include 0 in its range.
In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.
However, 0∉ S n- 1{\displaystyle 0\notin S^{n-1}}so there cannot be a continuous odd function whose range is S n- 1{\displaystyle S^{n-1}}.
Geometrically, the graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after rotation of 180 degrees about the origin.
The Borsuk- Ulam theorem is equivalent to the following statement:A continuous odd function from an n-sphere into Euclidean n-space has a zero.
Conversely, if it is incorrect, then there is a continuous odd function g: S n→ R n{\displaystyle g: S^{n}\to{\mathbb{R}}^{n}} with no zeroes.
If the theorem is correct,then it is specifically correct for odd functions, and for an odd function, g(- x)= g( x){\displaystyle g(- x)= g( x)} iff g( x)= 0{\displaystyle g(x)=0}.
Every function maybe uniquely decomposed as the sum of an even and an odd function, which are called respectively the even part and the odd part of the function; if one defines.
H(0)= 1/2 is often used since the graph then has rotational symmetry; put another way, H-1/2 is then an odd function. In this case the following relation with the sign function holds for all x: Math formula''H''(0){{=}}{{sfrac|1|2}}.
If a function is odd, the absolute value of that function is an even function. .