Limits of Trigonometric Functions.

[gabyoh23]

Limits of Trigonometric Functions. URGENT!

Homework Statement

Evaluate stackrel{lim}{x $$\rightarrow$$0}[/tex] [sin(\frac{2e}{x³}) \bullet (arctanx)]

Homework Equations

All I know is that the equation stackrel{lim}{x $$\rightarrow$$0}[/tex] $$\frac{sin x}{x}$$ = 1 might be helpful, but I'm not sure how to apply it to this particular problem.

The Attempt at a Solution

I talked to a friend of mine who's in Calc III, and she said that the whole limit would be equal to 0 since arctan(0) = 0, and sin$$\frac{2e}{x³}$$ is undefined, and the zero beats out the undefined value. This might be right, but how would I show that mathematically?

All help is greatly appreciated as I'm kind of in a crunch here :)

 

[Mark44]

Homework Statement

Evaluate stackrel{lim}{x $$\rightarrow$$0}[/tex] [sin(\frac{2e}{x³}) \bullet (arctanx)]

Homework Equations

All I know is that the equation stackrel{lim}{x $$\rightarrow$$0}[/tex] $$\frac{sin x}{x}$$ = 1 might be helpful, but I'm not sure how to apply it to this particular problem.

The Attempt at a Solution

I talked to a friend of mine who's in Calc III, and she said that the whole limit would be equal to 0 since arctan(0) = 0, and sin$$\frac{2e}{x³}$$ is undefined, and the zero beats out the undefined value. This might be right, but how would I show that mathematically?

All help is greatly appreciated as I'm kind of in a crunch here :)

Here's your corrected limit expression.

Evaluate $$lim_{x \rightarrow 0} sin(\frac{2e}{x^3}) arctanx$$

Your friend is leading you astray. It's not necessarily true that an expression tending to zero "beats out" an undefined value. What is true is that -1 <= sin(u) <= 1 for all real values of u.

 

[gabyoh23]

Thanks for correcting my formatting. I was in a rush, and I accidentally hit the "submit post" button before previewing it.

Thanks for the input!