Math Is Fun Forum

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?

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: 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?

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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mathland

Member

Registered: 2021-03-25

Posts: 444

Re: 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?

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?