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## #1 2013-12-18 01:42:00

MERTICH
Member
Registered: 2013-12-01
Posts: 18

### Squeeze Theorem

Use the squeeze theorem to determine

LIM                                [ 3 -sin(e^x)]/                 3 minus Sin(exp x) divided by
x--> infinity                     [V (X^2 + 2)]                   square root of ( x squared + 2)

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## #2 2013-12-18 01:48:31

MERTICH
Member
Registered: 2013-12-01
Posts: 18

### Re: Squeeze Theorem

I would also appreciate a stage by stage go...

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## #3 2013-12-18 01:55:05

zetafunc.
Guest

### Re: Squeeze Theorem

Use the fact that |sin(e[sup]x[/sup])| ≤ 1 and play with the inequality until you can bound your function.

## #4 2013-12-18 02:03:29

MERTICH
Member
Registered: 2013-12-01
Posts: 18

### Re: Squeeze Theorem

@ zetfunc , you mean like, since I know that no matter what, -1<sinx < 1 , so I should subsititute sin(e^x) with 1 and -1, in the expression to get my lower and upper bound?

Last edited by MERTICH (2013-12-18 02:10:09)

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## #5 2013-12-18 02:11:44

zetafunc.
Guest

### Re: Squeeze Theorem

The sine function, regardless of the argument (and as long as it is real), is always at least bounded between -1 and 1.

Do you see what we are trying to do?

## #6 2013-12-18 02:29:37

MERTICH
Member
Registered: 2013-12-01
Posts: 18

### Re: Squeeze Theorem

yes, but then how do you fit in the rest of the equation, or is it 2/( x^2 +2) </= f(x) </= 4/ (x^2 +2)  ?

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## #7 2013-12-18 02:44:24

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Squeeze Theorem

Yes, that is correct. The limit of the left and right bound are easy to get, so you should be able to get the original limit now.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #8 2013-12-18 03:08:23

zetafunc.
Guest

### Re: Squeeze Theorem

Yes (with the square root signs).

Now you just need to show that the limits of both bounds go to zero as x approaches infinity.

## #9 2013-12-18 04:02:47

MERTICH
Member
Registered: 2013-12-01
Posts: 18

### Re: Squeeze Theorem

that is to say the denominator power of both bounds is greater than the numerator power, such that when x approaches infinity, f(x) becomes zero.....thank you guys!

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