Posted by **miley** on Monday, September 19, 2011 at 11:05am.

Need help asap! what is the limit as x approaches 0 of -x/tan(3x) ?

- calculus -
**Reiny**, Monday, September 19, 2011 at 11:36am
You should have either proved or collected several basic trig limits

e.g.

limit sinx/x as x---> 0 = 1

also

lim tanØ/Ø as Ø ---> 0 = 1 which implies lim Ø/tanØ as Ø ---> 0 = 1

so let's make your question look like that

lim -x/tan(3x)

= lim -3x/(3tan(3x))

= lim (-1/3) [(3x)/tan(3x)] , (where 3x = Ø)

= lim (-1/3) [Ø/tanØ]

= (-1/3)(1)

= -1/3

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