prove this limit..c'mon math gurus

[Semidevil]

prove that the limit from x to +(infinite) of sin(x)/x is 0.

is this a l"hopital rule?

so if I differentiate, I get cos(x)/1....which doesn't say anything.

 

[Heisenberg]

I would just argue that as x->infinity, you have something O(1) divided by infinity, which is zero. But then again, I kinda sucked at limits.

 

[marcello]

It's not L'Hospital b/c it's not 0/0 or infinity/infinity

 

[Furyline]

squeeze theorem I think

since -1 <= sin(x) <= 1 .. and so on.

 

[TuxDave]

Originally posted by: Semidevil
prove that the limit from x to +(infinite) of sin(x)/x is 0.

is this a l"hopital rule?

so if I differentiate, I get cos(x)/1....which doesn't say anything.

-1/x < sin(x)/x < 1/x

lim x to +infinity of 1/x = 0.
lim x to +infinity of -1/x = 0.

Using the SQUEEZE theorem....

lim x to +infinity of sin(x)/x = 0.

 

[marcello]

Originally posted by: Heisenberg
I would just argue that as x->infinity, you have something O(1) divided by infinity, which is zero. But then again, I kinda sucked at limits.

That's not a way to prove it, it's just the rational way of thinking about it.

 

[TuxDave]

Originally posted by: Furyline
squeeze theorem I think

since -1 <= sin(x) <= 1 .. and so on.

Squeeze theorem, envelope theorem. eh... my only weakness in math was remember what was called what. I always knew what to do tho.

 

[marcello]

Originally posted by: TuxDave

Originally posted by: Semidevil
prove that the limit from x to +(infinite) of sin(x)/x is 0.

is this a l"hopital rule?

so if I differentiate, I get cos(x)/1....which doesn't say anything.

-1/x < sin(x)/x < 1/x

lim x to +infinity of 1/x = 0.
lim x to +infinity of -1/x = 0.

Using the envelope theorem....

lim x to +infinity of sin(x)/x = 0.

What's the envelope theorem? But nice proof

EDIT: NM, saw your edit

 

[Heisenberg]

Originally posted by: marcello

Originally posted by: Heisenberg
I would just argue that as x->infinity, you have something O(1) divided by infinity, which is zero. But then again, I kinda sucked at limits.

That's not a way to prove it, it's just the rational way of thinking about it.

Sorry. I'm a physicist, not a mathematician. 😉

 

[marcello]

Originally posted by: Heisenberg

Originally posted by: marcello

Originally posted by: Heisenberg
I would just argue that as x->infinity, you have something O(1) divided by infinity, which is zero. But then again, I kinda sucked at limits.

That's not a way to prove it, it's just the rational way of thinking about it.

Sorry. I'm a physicist, not a mathematician. 😉

Yeah, I'm a mathematician but I always do things your way. I hate proofs when it's so obvious what the answer is.

P.S. Unsurprisingly, I suck at math despite my major


EDIT: Clearly I suck at English too

 

[oboeguy]

It's also called the "sandwich theorem". Bah, no0bs. 😀

 

[bubbadu]

Isnt it LIMIT SIN(X) * LIMIT 1/x since sin(x) goes to some number, it loses as 1/x goes to zero really fast. I am not in a calc mod anyway tonight so i dont really know. All I know is that I have a fundmentals of computation test in 7 hours and never bought the book to study from. 😛

 

[Semidevil]

Originally posted by: marcello

Originally posted by: Heisenberg

Originally posted by: marcello

Originally posted by: Heisenberg
I would just argue that as x->infinity, you have something O(1) divided by infinity, which is zero. But then again, I kinda sucked at limits.

That's not a way to prove it, it's just the rational way of thinking about it.

Sorry. I'm a physicist, not a mathematician. 😉

Yeah, I'm a mathematician but I always do things your way. I hate proofs when it's so obvious what the answer is.

P.S. Unsurprisingly, I suck at math despite my major


EDIT: Clearly I suck at English too

wow, thank god i'm not the only math major who sucks at math....


btw, know any jobs for us math majors to consider? i'm having trouble.


edit: can someone explain again one more time why we can't use lhopital rule? confused.

 

[TuxDave]

Originally posted by: Semidevil
wow, thank god i'm not the only math major who sucks at math....
btw, know any jobs for us math majors to consider? i'm having trouble.

How about being an actuary?

 

[TuxDave]

Originally posted by: Semidevil
edit: can someone explain again one more time why we can't use lhopital rule? confused.

You l'hopital once.. and get stuck with

cos(x)/1

lim as x goes to +infinite of that is undefined

So you l'hopital again

-sin(x)/0... now you're screwed.

 

[Goosemaster]

Originally posted by: Semidevil

Originally posted by: marcello

Originally posted by: Heisenberg

Originally posted by: marcello

Originally posted by: Heisenberg
I would just argue that as x->infinity, you have something O(1) divided by infinity, which is zero. But then again, I kinda sucked at limits.

That's not a way to prove it, it's just the rational way of thinking about it.

Sorry. I'm a physicist, not a mathematician. 😉

Yeah, I'm a mathematician but I always do things your way. I hate proofs when it's so obvious what the answer is.

P.S. Unsurprisingly, I suck at math despite my major


EDIT: Clearly I suck at English too

wow, thank god i'm not the only math major who sucks at math....


btw, know any jobs for us math majors to consider? i'm having trouble.


edit: can someone explain again one more time why we can't use lhopital rule? confused.

"PRICECHECK IN DOGFOOD ISLE"





Concerning the problem, plug in values and see what happens. It will oscillate [sic] because that is the nature of sin and cos trigonometric functions

 

[marcello]

Originally posted by: Semidevil

Originally posted by: marcello

Originally posted by: Heisenberg

Originally posted by: marcello

Originally posted by: Heisenberg
I would just argue that as x->infinity, you have something O(1) divided by infinity, which is zero. But then again, I kinda sucked at limits.

That's not a way to prove it, it's just the rational way of thinking about it.

Sorry. I'm a physicist, not a mathematician. 😉

Yeah, I'm a mathematician but I always do things your way. I hate proofs when it's so obvious what the answer is.

P.S. Unsurprisingly, I suck at math despite my major


EDIT: Clearly I suck at English too

wow, thank god i'm not the only math major who sucks at math....


btw, know any jobs for us math majors to consider? i'm having trouble.


edit: can someone explain again one more time why we can't use lhopital rule? confused.

I just graduated and right now I'm a secretary....but I'm studying to become an actuary. Check it out, pays well, good hours. www.actuary.com

As for why you can't use L'Hospitals: To use it, the equation has to be 0/0 or infinity/infinity as you approach the limit. In your problem, sin oscillates so it doesn't approach anything and you can't use L'Hospitals.

 

[Semidevil]

Originally posted by: marcello

Originally posted by: Semidevil

Originally posted by: marcello

Originally posted by: Heisenberg

Originally posted by: marcello

Originally posted by: Heisenberg
I would just argue that as x->infinity, you have something O(1) divided by infinity, which is zero. But then again, I kinda sucked at limits.

That's not a way to prove it, it's just the rational way of thinking about it.

Sorry. I'm a physicist, not a mathematician. 😉

Yeah, I'm a mathematician but I always do things your way. I hate proofs when it's so obvious what the answer is.

P.S. Unsurprisingly, I suck at math despite my major


EDIT: Clearly I suck at English too

wow, thank god i'm not the only math major who sucks at math....


btw, know any jobs for us math majors to consider? i'm having trouble.


edit: can someone explain again one more time why we can't use lhopital rule? confused.

I just graduated and right now I'm a secretary....but I'm studying to become an actuary. Check it out, pays well, good hours. www.actuary.com

As for why you can't use L'Hospitals: To use it, the equation has to be 0/0 or infinity/infinity as you approach the limit. In your problem, sin oscillates so it doesn't approach anything and you can't use L'Hospitals.

cool cool. actually i"m studying for acturial science...but Im still on my first exam...so....need to find a temp job while stuying for it.

thanx for tip

 

[aplefka]

<obligatory 42 comment> 42 </obligatory 42 comment>

 

[vtqanh]

L'Hopital rule only works if the preconditions are met. You can only apply the rule to 0/0 or inf/inf limit
Change your major

EDIT: Sb already explained it above