# calculus

posted by .

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

• calculus -

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

## Similar Questions

1. ### Differential Calculus

use the rule that says limit of (e^h - 1)/h = 1 as h approaches 0 to show that the limit of [ln(x+h)-lnx]/h as h approaches 0 = 1/x, where x>0
2. ### Differential Calculus

use the rule that says limit of (e^h - 1)/h = 1 as h approaches 0 to show that the limit of [ln(x+h) -lnx]/h as h approaches 0 = 1/x, where x>0
3. ### Calculus

1. Use the Taylor series to calculate the limit. Problem: limit as x approaches 0 is equal to (1-cos(x))/(1+x-e^x). I did the problem out but I need help in seeing if its correct. limit as x approaches 0 is equal to (1-cos(x))/(1+x-e^x)= …
4. ### calculus - limits

limit as x approaches infinity; tan^(-1) (x^2 - x^4) any help is appreciated =D
5. ### Calculus

Could someone please help me with these questions;I was having trouble with these four questions. Evaluate each limit, if it exists, using any appropriate technique. 1.) The limit as u approaches 4; u^2-16/u^3-64 2.) The limit as x …
6. ### Calculus

FIND THE LIMIT As x approaches 0: tan 5 x/sin 25 x
7. ### Calculus

Evaluate the limit. The limit as x approaches 0 of (x-sin(x))/(x-tan(x))
8. ### calculus

If limit as delta x approaches 0 of tan(0+Δx)-tan(0)/Δx =1 which of the following is false: d/dx [tanx]=1 the slope of y = tan(x) at x = 0 is 1 y = tan(x) is continuous at x = 0 y = tan(x) is differentiable at x = 0
9. ### Calculus

Evaluate limit as x approaches 0 of: csc^2(7x)tan(2x^2)
10. ### Calculus

1. Evaluate the function at the given numbers (correct to six decimals places). Use the results to guess the value of the limit,or explain why it does not exist. F(t)=( t^(1/3) - 1)/(t^(1/2) - 1) ; t= 1.5,1.2,1.1,1.01,1.001; The limit …

More Similar Questions