Limit Help: limit [h -> infinity] (1/x)

[yargy]

Hey, so on my test there was a problem with this kind of concept. I put my answer as "undefined" because the variables didn't match. Do the variables have to match up between the approach and function? I asked my teacher and he said that it doesn't matter.

 

[stapel]

$\displaystyle \displaystyle \lim_{h\, \rightarrow\, \infty}\, \left(\dfrac{1}{x}\right)$

Hey, so on my test there was a problem with this kind of concept. I put my answer as "undefined" because the variables didn't match. Do the variables have to match up between the approach and function? I asked my teacher and he said that it doesn't matter.

Um... yes, the variables matter! If you'd been given "h/x", then the limit would have applied to one of the variables and not to the other, and the limit would have been "infinity". If you'd been given "x/h", then the limit value would have been something quite different.

Since "x" is expected ("required"?) in this case to be some fixed, but finite, value, the value of 1/x is finite (as long as x isn't equal to zero). What one does with h is irrelevant, in this particular case, to the value of 1/x.

I'm not quite sure how one might define the "answer" to this. I mean, the limit value will be the value of 1/x, whatever that is. If we know that x isn't zero, then 1/x is something finite and defined (as existing, in a mathematical sense), but unknown in its specifics. If we know nothing about the value of x, then it's hard to say. (And, of course, if we know that x = 0, then 1/x is undefined.)

My suspicion is that this is a typo, but the instructor is too proud to admit it (or too ignorant to understand it).

 

[pka]

Hey, so on my test there was a problem with this kind of concept. I put my answer as "undefined" because the variables didn't match.

If I were to construct a concept test using that question, then I would expect this answer:
$\displaystyle \displaystyle{\lim _{h \to \infty }}\left(\frac{1}{x}\right) = \frac{1}{x}$. Do you understand why that is correct?

 

[Bob Brown MSEE]

with one comment.

If I were to construct a concept test using that question, then I would expect this answer:
$\displaystyle \displaystyle{\lim _{h \to \infty }}\left(\frac{1}{x}\right) = \frac{1}{x}$. Do you understand why that is correct?

assuming that x is not a function of h.

 

[pka]

assuming that x is not a function of h.

There is absolutely about the question to even suggest that x is a function of h.
If that were the case, then it would be $\displaystyle \displaystyle{\lim _{h \to \infty }}\left( {\frac{1}{{x(h)}}} \right) = ?$ where $\displaystyle x(h)$ would have been fully defined.

If that were not the case, then the question would never gotten past a good editor.