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
Answer This Question
Related Questions
 calculus  If limit as delta x approaches 0 of tan(0+Δx)tan(0)/Δx =1 ...
 Calculus  Evaluate the limit. The limit as x approaches 0 of (xsin(x))/(xtan(...
 Calculus  Could someone please help me with these questions;I was having ...
 Calculus  Evaluate limit as x approaches 0 of: csc^2(7x)tan(2x^2)
 Calculus  FIND THE LIMIT As x approaches 0: tan 5 x/sin 25 x
 calculus  limits  limit as x approaches infinity; tan^(1) (x^2  x^4) any ...
 Calculus  1. Use the Taylor series to calculate the limit. Problem: limit as x ...
 Differential Calculus  use the rule that says limit of (e^h  1)/h = 1 as h ...
 Differential Calculus  use the rule that says limit of (e^h  1)/h = 1 as h ...
 Calculus  1. Evaluate the function at the given numbers (correct to six ...
More Related Questions