Undefined functions and limits

[thereddevils]

Homework Statement

The function f is defined by f(x)=(3sin(2x^2))/x^2 , x<0 . Find limit f(x) when x approaches 0 .

Homework Equations

The Attempt at a Solution

Of course , when i plug 0 in, f(x) is undefined . How do i make into a form where i can plug the 0 in without the function being undefined

 

[irycio]

Well, I assume you know what $$\lim\limits_{x \to 0} \frac{sinx}{x}$$ is. That applies to x being more complex than a single number as well.
More generally, my suggestion is to read about de L'Hospital's rule that allows you to calculate limes when you encounter the situation $$\frac{0}{0}$$ or $$\frac{\infty}{\infty}$$.

 

[thereddevils]

Well, I assume you know what $$\lim\limits_{x \to 0} \frac{sinx}{x}$$ is. That applies to x being more complex than a single number as well.
More generally, my suggestion is to read about de L'Hospital's rule that allows you to calculate limes when you encounter the situation $$\frac{0}{0}$$ or $$\frac{\infty}{\infty}$$.

ok , i will try to read up that rule but is there any elementary method to evaluate the limit for that function ?

 

[Cyosis]

Can you write down the derivative of sin(x) by using the definition of the derivative? Compare this to the limit you're asked to compute.

 

[HallsofIvy]

ok , i will try to read up that rule but is there any elementary method to evaluate the limit for that function ?

If you are referring to $\lim_{x\to 0} sin(x)/x$, how you prove that depends on exactly how you are defining sin(x).

 

[thereddevils]

Can you write down the derivative of sin(x) by using the definition of the derivative? Compare this to the limit you're asked to compute.

you meant this :

$$f'(x)=\lim_{\delta x\rightarrow 0}(\frac{\sin (x+\delta x)-\sin x}{\delta x})$$ ?

 

[Cyosis]

Yes, how can you modify that expression so that it is equal to your limit problem?