Question #83a91

1 Answer
Deepak Pandey
Sep 16, 2017

#lim x rarr oo (x+sin^3x)/(2x-1)=1/2#

Explanation:

We have #lim x rarr oo (x+sin^3x)/(2x-1)#
Now #(x+sin^3x)/(2x-1)#
#=1/(2-1/x)+sin^3x/(2x-1)#
Now as # x rarr oo , 1/x rarr 0 and 1/(2x-1) rarr 0 and sin^3x # is somewhere between #-1 and 1 # which is finite , hence if we multiply #sin^3x# by a number approaching zero then we the product will approach zero.
#:.lim x rarr oo (x+sin^3x)/(2x-1)=1/2#

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