From Wikipedia, the free encyclopedia
This template uses Lua :
{{ Infobox mathematical function
| name =
| image = | imagesize = <!--(default 220px)--> | imagealt =
| parity = | domain = | codomain = | range = | period =
| zero = | plusinf = | minusinf = | max = | min =
| vr1 = | f1 = | vr2 = | f2 = | vr3 = | f3 = | vr4 = | f4 = | vr5 = | f5 =
| asymptote = | root = | critical = | inflection = | fixed =
| notes =
}}
Pairs VR1-f1, f1-VR2, etc. are used for labeling specific value functions. Suppose a function at the point e has a value of 2e and that this point is because of something specific. In this case you should put that as VR1 = eand f1 = 2e. For the next point is used a couple of VR2-f2, etc. If you run out of points (five currently available), ask for more.
Variables heading1, heading2, heading3 define whether some of the headlines basic properties, specific values, etc. be displayed. If you do not want a title to be displayed, simply delete the variable from the template. Set the value of the variable to 0 or anything will not prevent the display title.
Variables plusinf and minusinf indicate the value function at + ∞ and - ∞.
root is the x-intercept, critical is the critical point(s), inflection is inflection point(s)
fixed is fixed point (s)
The code below produces the box opposite:
Sine General definition
sin
(
α
)
=
opposite
hypotenuse
{\displaystyle \sin(\alpha )={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}}
Motivation of invention Indian astronomy Date of solution Gupta period Fields of application Trigonometry , Integral transform , etc.Domain (−∞ ∞ a Image [−1, 1] a Parity odd Period 2π At zero 0 Maxima (2k π + π / 2 , 1)b Minima (2k π − π / 2 , −1) Root k π Critical point k π + π / 2 Inflection point k π Fixed point 0 Reciprocal Cosecant Inverse Arcsine Derivative
f
′
(
x
)
=
cos
(
x
)
{\displaystyle f'(x)=\cos(x)}
Antiderivative
∫
f
(
x
)
d
x
=
−
cos
(
x
)
+
C
{\displaystyle \int f(x)\,dx=-\cos(x)+C}
Other Related cos, tan, csc, sec, cot Taylor series
x
−
x
3
3
!
+
x
5
5
!
−
x
7
7
!
+
⋯
=
∑
n
=
0
∞
(
−
1
)
n
(
2
n
+
1
)
!
x
2
n
+
1
{\displaystyle {\begin{aligned}x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \\[8pt]&=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}x^{2n+1}\\[8pt]\end{aligned}}}
Generalized continued fraction
x
1
+
x
2
2
⋅
3
−
x
2
+
2
⋅
3
x
2
4
⋅
5
−
x
2
+
4
⋅
5
x
2
6
⋅
7
−
x
2
+
⋱
.
{\displaystyle {\cfrac {x}{1+{\cfrac {x^{2}}{2\cdot 3-x^{2}+{\cfrac {2\cdot 3x^{2}}{4\cdot 5-x^{2}+{\cfrac {4\cdot 5x^{2}}{6\cdot 7-x^{2}+\ddots }}}}}}}}.}
{{ Infobox mathematical function
| name = Sine
| image = Sinus.svg
| parity = odd | domain = (-∞,∞) | range = [-1,1] | period = 2π
| zero = 0 | plusinf = | minusinf = | max = ((2k+½)π,1) | min = ((2k-½)π,-1)
| asymptote = | root = kπ | critical = kπ-π/2 | inflection = kπ | fixed = 0
| notes = Variable k is an [[ integer ]] .
}}
Math templates
Functions
Numeral systems
mvar individual italicized maths variables in normal text
overline underline a line set above/below a sequence of characters overarc an arc set above a sequence of characters
overset underset arbitrary characters/diacritics set above/below one another pars parentheses that can be resized ( ∑ ) sfrac "standing" or upright fractions 3 / 5 (use in maths/science articles instead of{{fraction }}
sub sup su subscripts and superscripts tmath Wrap TeX <math> tags tombstone symbol indicating the end of a proof val measurement values, uncertainties and units vec various overarrows, underarrows, etc.
![{\displaystyle {\begin{aligned}x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \\[8pt]&=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}x^{2n+1}\\[8pt]\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91b7e722b0e78f16453f0b08592125448c3a0d8e)
