What is the limit of $sin [\frac{π x}{2 - 3 x}]$ $sin[(pix) /(2-3x)]$ as x approaches infinity?

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Answer 1 · 2015-05-19T18:42:22

to solve for $lim_(x->oo) sin((pix)/(2-3x))$

we simplify by dividing the inner function by $x$

$lim_(x->oo) sin(pi/((2/x)-3))$

we know that $color(red)( lim_(x->oo) 2/x= 0 )$

thus we get:

$= sin(pi/(0-3)) = sin(-(pi/3))$

$= - sin(pi/3)$

$=- (sqrt(3)/2)$

What is the limit of sin[(pix) /(2-3x)]sin[πx2−3x]sin[(pix) /(2-3x)] as x approaches infinity?