Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

Basic limit proof

Show that

It said as a hint to use the same proof but for sine to help, but I'm not really sure how to do that...

Last edited by Identity (2007-07-08 23:40:23)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Basic limit proof

Are you allowed to use L'Hopital? That's the route I'd take.

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Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Basic limit proof

Actually I just figured out how to prove, I used

, divided through by tan, then took the limit of cos.

But I would be happy if you could tell me what the L'Hopital is?

HallsofIvy

Guest

Re: Basic limit proof

Actually I just figured out how to prove, I used

, divided through by tan, then took the limit of cos.

But I would be happy if you could tell me what the L'Hopital is?

That seems a bit complicated!  Just write

  L'Hopitals rule says that if f(x)-> 0, g(x)-> 0 as x-> a, then

  That's much more "sophisticated" than is needed here.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Basic limit proof

I believe you are trying to use the squeeze theorem, no?  I don't see how dividing through by tangent in that inequality will give you some form of tan(theta)/theta.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Basic limit proof

dividing by tanθ

reciprocating

Hence, as

is squeezed in,

Is that right?

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Basic limit proof

You are doing things without justification.  How do you know that:

What happens when you divide by a negative in an inequality?  What are you actually doing when you take a reciprocal?  You kind of just gloss over these things.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Basic limit proof

That was an inequality used in a previous proof (the one for sine) so I thought I might borrow it

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Basic limit proof

You can't just borrow and put things like that.
After borrowing you should manipulate it a little bit, fit it to your case, so nobody realize what had happened.

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