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