# limits of slopes?

• December 20th, 2011, 08:30 PM
brody
limits of slopes?
I know there are limits like "as x approaches infinity, y approaches 2.718..."

But could you say that a function approaches a certain slope?

For example, , as x approaches +∞, the function approaches a slope of 1.
• December 28th, 2011, 06:16 AM
Markus Hanke
Quote:

Originally Posted by brody
I know there are limits like "as x approaches infinity, y approaches 2.718..."

But could you say that a function approaches a certain slope?

For example, , as x approaches +∞, the function approaches a slope of 1.

What you are trying to say is that the original function's first derivative f'(x) ( which is the function's slope ) approaches 1 for x -> infinity. It is still a simple limit.
• December 28th, 2011, 07:01 AM
theQuestIsNotOver
You're trying to perfect a circle, right, as a graphed algorithm?
• December 28th, 2011, 09:26 AM
brody
@Markus Hanke: I mean instead of saying x-->∞, f(x)-->∞ I would say for slope x-->∞, "slope"-->1. As the limits I've seen always refer to x values and their functions. Never a reference to slope. The slope of any non-linear function, I believe, is inconstant. So, you could say that, although there is no actual defined slope for the entire function, it approaches a certain, predictable steepness on the graph.

@theQuestIsNotOver: Not at all. :)
• December 28th, 2011, 09:56 AM
Markus Hanke
Quote:

Originally Posted by brody
@Markus Hanke: I mean instead of saying x-->∞, f(x)-->∞ I would say for slope x-->∞, "slope"-->1. As the limits I've seen always refer to x values and their functions. Never a reference to slope. The slope of any non-linear function, I believe, is inconstant. So, you could say that, although there is no actual defined slope for the entire function, it approaches a certain, predictable steepness on the graph.

@theQuestIsNotOver: Not at all. :)

You are wrong, the slope of the function is exactly defined; f'(x) = (-1/x^2)+1. It is defined for all x <> 0 ( although of course not constant ), and its limit for x -> infinity is 1; this is elemental calculus. May I ask what the point in this thread actually is ?
• December 28th, 2011, 12:53 PM
brody
Quote:

May I ask what the point in this thread actually is ?
The point of this thread actually is for me to learn from the question I had presented as a speculative idea and you had answered it. I was never familiar with any reference to limits of slopes and I wondered if there was such a concept. As you answered, indeed there is in elementary calculus. Thank you.
• December 29th, 2011, 02:32 AM
Markus Hanke
Quote:

Originally Posted by brody
Quote:

May I ask what the point in this thread actually is ?
The point of this thread actually is for me to learn from the question I had presented as a speculative idea and you had answered it. I was never familiar with any reference to limits of slopes and I wondered if there was such a concept. As you answered, indeed there is in elementary calculus. Thank you.

No problem...remember the slope of any continuous and differentiable ( single variable ) function is just simply its first derivative, and you can use that to form limits in the usual way; so the "limit of slope" is best expressed as a limit of the first derivative.