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#1 2021-04-03 10:49:54

mathland
Member
Registered: 2021-03-25
Posts: 444

Limit of Rational Function...3

Find the limit of 5/(x^2 - 4) as x tends to 2 from the right side.

Approaching 2 from the right means that the values of x must be slightly larger than 2.

I created a table for x and f(x).

x...............2.1.....2.01................2.001
f(x)...........12......124.68............1249.68

I can see that f(x) is getting larger and larger and possibly without bound.

I say the limit is positive infinity.

Yes?

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#2 2021-04-03 17:46:21

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Limit of Rational Function...3

mathland wrote:

Find the limit of 5/(x^2 - 4) as x tends to 2 from the right side.

Approaching 2 from the right means that the values of x must be slightly larger than 2.

I created a table for x and f(x).

x...............2.1.....2.01................2.001
f(x)...........12......124.68............1249.68

I can see that f(x) is getting larger and larger and possibly without bound.

I say the limit is positive infinity.

Yes?

Approaching 2 from the right means that the values of x must be slightly larger than 2.

Indeed.

Looks all good to me here.

Last edited by Mathegocart (2021-04-03 17:47:59)


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#3 2021-04-03 23:57:26

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Limit of Rational Function...3

Mathegocart wrote:
mathland wrote:

Find the limit of 5/(x^2 - 4) as x tends to 2 from the right side.

Approaching 2 from the right means that the values of x must be slightly larger than 2.

I created a table for x and f(x).

x...............2.1.....2.01................2.001
f(x)...........12......124.68............1249.68

I can see that f(x) is getting larger and larger and possibly without bound.

I say the limit is positive infinity.

Yes?

Approaching 2 from the right means that the values of x must be slightly larger than 2.

Indeed.

Looks all good to me here.


Excellent. 

Question:

Can this function be separated into two parts?

In other words, can 5/(x^2 - 4) be expressed as (5/1)(1/(x^2 - 4))? If so, the product rule for limits does apply, right?

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