Changes

Sinc function

, 12:54, 4 September 2011
Key data
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| [[period]] || none; the function is not periodic
|-
| [[horizontal asymptote]]s || $y = 0$, i.e., the $x$-axis. This is because $\lim_{x \to \pm \infty} \frac{\sin x}{x} = 0$, which in turn can be deduced from the fact that the numerator is bounded while the magnitude of the denominator approaches $\infty</matH>. |- | [[local maximum value]]s and points of attainment || The local maxima occur at points [itex]x$ satisfying $\tan x = x$ and $x in [2n\pi,(2n + 1)\pi]$ or $x \in [-(2n + 1)\pi,-2n\pi]$ for $n$ a positive integer.<br> There is an anomalous local maximum at $x = 0$ with value 1. Apart from that, the other local maxima occur at points of the form $\pm(2n\pi + \alpha_n)$ where $\alpha_n$ is fairly close to $\pi/2$ for all $n > 0$. The local maximum value at this point is slightly more than $1/(2n\pi + \pi/2)$.
| [[point of inflection|points of inflection]] || {{fillin}}
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| [[derivative]] || $\operatorname{sinc}'x = \left\lbrace \begin{array}{rl} 0, & x = 0 \\ \frac{x \cos x - \sin x}{x^2} , & x \ne 0\\\end{array}\right.$
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| [[antiderivative]] || the [[sine integral]] (''this is defined as the antiderivative of the sinc function that takes the value 0 at 0'')
|}

==Graph==
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