limits: meaning of "limit is 0 as x approaches neg. inf

[katie9426]

What does it mean if the limit as x approaches negative infinity of f(x) equals 0? Does it create a vertical tangent line? How owuld you find the equation of that tangent line?? Thanks!

 

[skeeter]

Re: limits

What does it mean if the limit as x approaches negative infinity of f(x) equals 0? Does it create a vertical tangent line? How owuld you find the equation of that tangent line?? Thanks!

\(\displaystyle \L \lim_{x\rightarrow -\infty} f(x) = 0\) describes the "left" end behavior of f(x) ... namely that values of f(x) for large negative values of x approach the value y = 0 ... therefore, y = 0 is a horizontal asymptote in that direction.

a relatively simple example of such a function with that behavior would be \(\displaystyle \L y = e^x\).

 

[pka]

Does it have to be asymptotic?
\(\displaystyle \lim _{x \to - \infty } \left( {\frac{{\sin (x)}}{x}} \right) = 0.\)

 

[katie9426]

It doesn't say anything about that. It just says find the equation for the vertical tangent line.

 

[pka]

It doesn't say anything about that. It just says find the equation for the vertical tangent line.

There would be no vertical tangent line in the case. As Skeeter pointed out there may be a horizontal one but as I pointed out that is not necessary.