Problem: Find the following limits if they exist.(adsbygoogle = window.adsbygoogle || []).push({});

a) lim x->Infinity (x-sin(x))/x

Work done so far: g(x) = x which goes to infinty as x goes to infinity, thus applying L'Hospitals Rule the limit must equal:

1-cos(x) / 1 = 1-cos(x) as x approaches infinity.

Obviously... cos(x) oscillates from 1 to -1... not giving us a real limit.

Alternative:

(x-sin(x))/x = 1 - sin(x)/x = 1 - (1/x)sin(x) as X approachs infinity this limit becomes 1 - 0 = 1.

My problem is that the back of the book tells me the answer is 0... I have no clue how they got this and I was wondering if anyone could give me a push in the right direction.

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# Limit of (x-sin(x))/x

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