Problem involving limits

Calculus
Tutor: None Selected Time limit: 1 Day

Find the limit of

lim (sin x - x)/x^3

As x approaches 0?

Please help.

      

Feb 16th, 2015

By L'Hopital's rule, we need to find the lim as x approaches 0 of (cos x - 1)/(3x^2). (Note we take the derivative of the numerator and denominator. 

We can repeat this again to find that this limit is equivalent to lim as x approaches 0 of (-sin x)/(6x) which is equal to lim as x approaches 0 of (-cosx)/6 = -1/6. 

Feb 16th, 2015

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