Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

sinh x

Hi, I have a question about the sinh function. Is it true that:

Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: sinh x

Hi Au101;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zetafunc.

Guest

Re: sinh x

Sorry if this answer is stupid, but wouldn't it tend to negative infinity since you get an increasing term in the numerator due to the -e[sup]-x[/sup]...? e[sup]x[/sup] would tend to 0 but you'd still end up with smaller and smaller values as x tends to negative infinity, right?

zetafunc.

Guest

Re: sinh x

I think the -e^-x term would be eliminated if x tends to negative infinity, so you're just left with (e^x)/2.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: sinh x

I believe that you are indeed both right. I was looking at the graph of y = sinh x, though, which, for large, negative values of x, approaches the graph of:

As we can see, because:

Now, my textbook wrote:

But I really didn't like this way of putting it and I quite like limits and asymptotic analysis and such areas and so I thought I'd try to make use of them, but we don't cover them in much detail and I have limited (poor pun) experience of using minus infinity, so I just wanted to check that this was a valid way of expressing the idea.

Last edited by Au101 (2011-08-19 12:13:07)

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: sinh x

Hi Au101,

You may write it as -∞

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: sinh x

Okay, thanks everyone

On a related note, if you can express the idea that:

As:

How would you express:

Thanks

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: sinh x

Hi,

Maybe

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: sinh x

Hmmm, thanks gAr - I think you may well be right about that one.

Okay, well, can I ask some advice on phrasing. I'm writing an introduction to hyperbolic functions, and I'm analysing the graph of y = sinh x. Two of the features which I want to bring out are:

And:

Since I am talking about the graph, it's really important to me to bring out the fact that for large, negative values, sinh x approaches that function (1/2e^(-x)). I could just leave it in words, as I have it here, but the trouble is, when it comes to explaining why the graph of y = tanh x has asymptotes at y = 1 and y = -1, I am going to have a very confusing sentence or two, so what I'd really like is some advice on how to phrase it. I was going to use the limits notation I had all the way back up in post 1, but I'm not sure if that's the best option, so I tried the asymptotic equivalence notation we've just been looking at - but that doesn't seem to work that well either. I think you're probably right, gAr, but is it likely to be that well understood or commonly used?

So, what do you guys think? Should I just leave it in words and sacrifice the simple sentence structure?

Thanks

Last edited by Au101 (2011-08-22 13:57:56)