If $f (x) = \frac{sin ([x] π)}{x^{2} + x + 1}$ , where $[x]$ denotes the integral part of $x$ . Show that $f (x)$ is a constant function.

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Solution

$f (x) = \frac{sin ([x] π)}{x^{2} + x + 1}$
$[x] =$ integer
$∴ [x] π = n π$
$∴ sin n π = 0$
$∴ f (x) = 0 =$ constant function

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If f(x)=sin([x]π)x2+x+1, where [x] denotes the integral part of x. Show that f(x) is a constant function.

f(x)=sin([x]π)x2+x+1[x]=integer ∴[x]π=nπ ∴sinnπ=0 ∴f(x)=0= constant function

If $f (x) = \frac{sin ([x] π)}{x^{2} + x + 1}$ , where $[x]$ denotes the integral part of $x$ . Show that $f (x)$ is a constant function.

$f (x) = \frac{sin ([x] π)}{x^{2} + x + 1}$
$[x] =$ integer
$∴ [x] π = n π$
$∴ sin n π = 0$
$∴ f (x) = 0 =$ constant function