# Limits Involving Trigonometric Functions

• Feb 1st 2010, 07:06 PM
amm345
Limits Involving Trigonometric Functions
I am reviewing for my midterm and realize that I was out sick when the class covered trigonometric functions. Any explanation on how to solve these would be great!
-limx->0 (x/arcsinx)
-limx->infinity (xarccotx)
• Feb 1st 2010, 07:08 PM
Drexel28
Quote:

Originally Posted by amm345
I am reviewing for my midterm and realize that I was out sick when the class covered trigonometric functions. Any explanation on how to solve these would be great!
-limx->0 (x/arcsinx)
-limx->infinity (xarccotx)

Hint:

$\displaystyle \frac{1}{f'(x)}$

and

Let $\displaystyle x=\frac{1}{z}$.
• Feb 1st 2010, 07:37 PM
Pulock2009
how about using L'Hospital's rule? that makes it a lot easier. by the way wats the answer.is the first one =1???
• Feb 1st 2010, 07:38 PM
amm345
I thought the first one was 0? and I already tried L'Hopitals and I still couldn't figure out.
• Feb 1st 2010, 07:42 PM
Pulock2009
u need to differentiate the numerator and the denominator separately.then the numerator becomes 1.and the denominator becomes 1/sqrt(1-x^2).now put the limits and u should get 1.
• Feb 1st 2010, 07:44 PM
amm345
How about when I can't do it seperately?
Like for limx->0 x/arccosx?
• Feb 1st 2010, 07:51 PM
Pulock2009
i donot get the second one. limit doesnot exist for the second one unless x->0.
• Feb 1st 2010, 07:52 PM
amm345
x does tend to 0, isn't the limit equal to 0?
• Feb 1st 2010, 07:57 PM
Pulock2009
no. limit for the second one is also 1.provided ,ofcourse,if x->0.
• Feb 1st 2010, 07:59 PM
Pulock2009
u must learn your differentiation formulas well.:D