Dividing Functions Questions

What do you get when plugging 0 into F(X) ?

 

Hi CanadianEh!

At x = 0, obviously, it's 0/0, which is undefined (it's known as an "indeterminate form"), so yes in that sense there's a hole …

of course, F(x) does tend to a limit at as x -> 0

 

uhh?

wot's an oblique asymptote? ​

 

The function continues to have a defined value as you get arbitrarily close to zero, thus the limit as x->0 is defined. The function itself is undefined only exactly at zero.

- Warren

 

Try graphing x/sin(x) and you'll only see vertical asymptotes when the denominator, or sin(x), is 0.
As far as I know, a rational function P(x)/Q(x) where P and Q are polynomials has an oblique asymptote only when the degree of the numerator is one larger than that of the denominator. In x/sin(x) you have a transcendental function in the denominator.

 

Still totally confused as to why this is called an asymptote instead of a tangent.

Anyway I can't see how it's slanting ……

what is lim_{x -> 0} x/sinx ?

 

That's right.

A slant asymptote
http://home.att.net/~srschmitt/precalc/precalc-fig12-03.gif [Broken]

 

So that's only at infinity?

 

and also negative infinity if the domain goes there too.

 

tiny-tim, the word "asymptote" was wrong here. He intended "tangent" as you suggested. Because there is a "hole" at x= 0, there is no tangent there.