What is the limit of #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)#