Question #83a91

1 Answer
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