LIMITS HELP PLEASE :D (1 Viewer)

[Lindurr]

Hi I was just a bit confused and wanted some clarification -
what is the limit as x approaches infinity of the function cos(x)

and

Why does 1-sin(x) have no limit as x approaches infinity?

Thankyou so much for the help

 

[nightweaver066]

When you're taking limits of functions, what you're finding is what f(x) value the function is approaching.

However, in these cases, e.g. f(x) = cosx, when taking the limit as x -> infinity, knowing that cosx is a periodic function that doesn't tend towards any f(x) value, it does not have a limit.

This is similar for f(x) = 1 - sinx, as it is a periodic function that doesn't tend towards any f(x) value towards infinity.

 

[Shadowdude]

Well, draw those functions. You'll see why it has no limit.

They'll forever keep oscillating between -1 and 1, or in the case of the 1-sin(x), 0 and 2.

 

[D94]

Cos(x) and Sin(x) will go as high as 1 and as low as -1 and will keep on oscillating infinitely, touching both upper and lower bounds to infinity. Hence it cannot have a limit.

 

[Lindurr]

Hi thank you so much

Another question to clarify: so why does the limit as x-> infinity of x+cosx = infinity?

Sorry Im finding all this a bit confusing

 

[Shadowdude]

Again draw the graph. Does it converge to a certain finite limit? Clearly not.

See: http://www.wolframalpha.com/input/?i=x+++cos(x)

So the limit doesn't exist.

 

[D94]

Hi thank you so much

Another question to clarify: so why does the limit as x-> infinity of x+cosx = infinity?

Sorry Im finding all this a bit confusing

Because the limit of x as x tends to infinity is infinity, and since cos(x) oscillates between +/- 1, it makes little impact on the infinity, hence it's infinity.

 

[nightweaver066]

Hi thank you so much

Another question to clarify: so why does the limit as x-> infinity of x+cosx = infinity?

Sorry Im finding all this a bit confusing

As x-> infinity, -1 <= cosx <= 1 and x -> infinity, so the value of cosx becomes negligible.

So limit as x -> infinity, x + cosx = infinity

 

[Drongoski]

Hi I was just a bit confused and wanted some clarification -
what is the limit as x approaches infinity of the function cos(x)

and

Why does 1-sin(x) have no limit as x approaches infinity?

Thankyou so much for the help

1) Before you can understand all this you need to understand what a limit is. Because the treatment for HSC maths is intuitive (nothing wrong with that) rather than rigorous, then unless your teacher explained the concept of a limit sufficiently well, you will have only a wobbly understanding of what it is (even at the intuitive level).

2) saying "the limit of f(x) as x goes to infinity is 5", say, is very different from saying "the limit of g(x) as x goes to 7 is infinity". Both are called limit - but the 1st one is a proper limit - the function tends to a fixed number, '5' in this case. In the latter case, the function does to tend to a fixed number - infinity is not a fixed number.

I'd love to give a fuller explanation of the concept of limit in any future "BoS Group Study Session" like the one we had at Parramatta Library about 10 days ago.

 

[Demento1]

1) Before you can understand all this you need to understand what a limit is. Because the treatment for HSC maths is intuitive (nothing wrong with that) rather than rigorous, then unless your teacher explained the concept of a limit sufficiently well, you will have only a wobbly understanding of what it is (even at the intuitive level).

2) saying "the limit of f(x) as x goes to infinity is 5", say, is very different from saying "the limit of g(x) as x goes to 7 is infinity". Both are called limit - but the 1st one is a proper limit - the function tends to a fixed number, '5' in this case. In the latter case, the function does to tend to a fixed number - infinity is not a fixed number.

I'd love to give a fuller explanation of the concept of limit in any future "BoS Group Study Session" like the one we had at Parramatta Library about 10 days ago.

I've been told by Carrotsticks that he and Annugurl plan to hold another study session in the next school holidays.