Limit as x approaches zero (1/x-1/tanx)

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1. massage the form to

1/x - cosx/sinx
= (cosx-x)/(x*sinx)

and apply l'Hospital's Rule

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posted by Steve
2. That is where I am confused ...

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posted by Sarah
3. Oops. A typo. Should be
(x*cosx-sinx)/(x*sinx)

just take derivatives, top and bottom. The limit is the same as for

(-x*sinx+cosx-cosx)/(sinx + xcosx)
= (-x sinx)/(sinx + x cosx)

still -> 0/0, so do it again:

(-sinx - x*cosx)/(cosx + cosx - x*sinx)
-> 0/2 = 0

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posted by Steve

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