limit

0 makes sense to me, I dunno why you''d bother to use a computer program. This is why analysis should be taught thoroughly to everyone. It could be interesting to see why you''re getting the wrong answer with those programs though.

inf - inf does not equal 0.

Your limit does not have a value since sin(x) does not approach any value as x->+inf.

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Colin Jeanne | Invader''s Realm
"I forgot I had the Scroll Lock key until a few weeks ago when some asshole program used it. It even used it right" - Conner McCloud

You really shouldn''t post school questions on this website. Since it''s summer, though, you may not be. So I''ll answer the question:

You have this as x goes to infinity:
sin(x+1/x)-sin(x) -> sin(1)-sin(x)
-> sin(1)-[-1,1]...

Thus, the limit does not exist.

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All polynomials are funny - some to a higher degree.
Furthermore, polynomials of degree zero are constantly funny.

The answer Maple and Mathematica give is not wrong. It simply reflects the fact that the limit does not exist, and the function oscillates within the range [-2,2].

[edited by - Mastaba on June 11, 2004 4:44:19 PM]

The limit exists, and it is 0.

Let's see the proof:

K = sin(x+1/x) - sin(x) =

sin(x)*cos(1/x)+cos(x)*sin(1/x) - sin(x) =

sin(x)*(cos(1/x)-1) + cos(x)*sin(1/x)

1/x -> 0,
cos(1/x) -> 1,
sin(1/x) -> 0,
sin(x) is in [-1;1],
cos(x) is in [-1;1],
so K -> 0 + 0 = 0


[edited by - szinkopa on June 11, 2004 5:02:24 PM]

sin(x+1/x) and sin((x+1)/x) are very different things...

the first one is what was actually posted, and the second one is what I actually read, and what I think most other people read too

given the nice simple arguments used earlier, instead of szink''s expansion, we have:

x -> infinity
1/x -> 0
x+1/x -> x
sin(x+1/x) -> sin(x)
sin(x+1/x) - sin(x) -> sin(x) - sin(x) -> 0

Nice!

This is a lesson in why spacing and a pencil are very important tools to mathematicians! ;-)

Yea, you''re going to have sin(x+ (1/x)) - sin(x) is going to goto zero. (Which is quite obvious, to anyone with a reasonable amount of calculus).

Scout

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All polynomials are funny - some to a higher degree.
Furthermore, polynomials of degree zero are constantly funny.

Closing thread. The Forum FAQ provides guidelines for this type of question.

Graham Rhodes
Principal Scientist
Applied Research Associates, Inc.