Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Limit of Rational Function...2

Find the limit of (3x)/(x - 2) as x tends to 2 from the left side.

Approaching 2 from the left means that the values of x must be slightly less than 2.

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

x...............0.....0.5.....1.....1.5
f(x)...........0......-1.....-3......-9

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

I say the limit is negative infinity.

Yes?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Limit of Rational Function...2

hi mathland

That's exactly how I'd do this and yes, you are correct.

You can also use the graph to see what is happening.

Here's a link to a function grapher https://www.mathsisfun.com/data/function-grapher.php

You'll need to use the zoom control to zoom out enough to see what happens either side of x =2.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Limit of Rational Function...2

hi mathland

That's exactly how I'd do this and yes, you are correct.

You can also use the graph to see what is happening.

Here's a link to a function grapher https://www.mathsisfun.com/data/function-grapher.php

You'll need to use the zoom control to zoom out enough to see what happens either side of x =2.

Bob

Thank you, Bob. Another member said that splitting the rational function into two functions and then applying the product rule for limits is a good algebraic approach. I concur. Using tables takes too much of my time. Time is limited for me as a full-time overnight employee. Thus, I am always searching for an easy approach to solve textbook problems.

Thanks for the Grapher link. Ever heard of Desmos? It's a great online graphing calculator. Tell me, how do I upload images to my posts on this website? It is often easier for me to screen shot a textbook page showing the question(s) that I need help with.

I start learning the derivative today or tomorrow.  Currently in Chapter 1, Section 1.6, which involves the epsilon-delta definition of a limit. Section 1.6 is the hardest section so far in Chapter 1. Expect questions in terms of using the Formal Definition of a Limit later on today. Happy Resurrection Sunday to you. Notice I didn't say Happy Easter.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Limit of Rational Function...2

hi mathland,

One of the advantages of the forum is that you may get different methods for solving a problem and you are free to choose what suits you best.

For the limit problems you have posted so far I find it easy enough to consider just left (or right) of the x value and so determine whether the y goes to + or - infinity.  I can do that 'in my head' so it's quick and easy.  Later the problems will be harder and you'll need other techniques.

A long time ago on an old server it was possible to upload small images directly to the server.  But we lost that with an upgrade.  The forum server has been upgraded again very recently.  Haven't found out if image upload is possible; I'll ask.

What I've done for a while is uploaded to imgur.com  You can get the bccode for imbedding into your post and then the image appears at the point where you put the code.

That's what I did here http://www.mathisfunforum.com/viewtopic … 79#p417979 to show the scatter plot.

The link is this:

https://i.imgur.com/dPeu971.gif

I'm not sure if you can view that directly, as you won't be logged in to my account, but it shows the method.  edit.  Tried it and it does load.

Please be careful copying parts of a textbook to the forum.  A while back we had a complaint from an on-line teaching company because a student had posted a worksheet.  It is a breach of copyright so we asked the student to (1) only put a single question into a request for help and (2) to type the question in their own words to avoid direct copying.  In the UK the copyright law allows copies when used for fair criticism so perhaps you could preface your post with a suitable comment such as 'This comes from <name of book> which I really like as it has good explanations and questions'

Is it Easter?  The days just blur into one what with lockdown restrictions.  Arrh! Just noticed I've got a choccy egg in front of me.  That must mean something.

Best wishes to you too.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Limit of Rational Function...2

hi mathland,

One of the advantages of the forum is that you may get different methods for solving a problem and you are free to choose what suits you best.

For the limit problems you have posted so far I find it easy enough to consider just left (or right) of the x value and so determine whether the y goes to + or - infinity.  I can do that 'in my head' so it's quick and easy.  Later the problems will be harder and you'll need other techniques.

A long time ago on an old server it was possible to upload small images directly to the server.  But we lost that with an upgrade.  The forum server has been upgraded again very recently.  Haven't found out if image upload is possible; I'll ask.

What I've done for a while is uploaded to imgur.com  You can get the bccode for imbedding into your post and then the image appears at the point where you put the code.

That's what I did here http://www.mathisfunforum.com/viewtopic … 79#p417979 to show the scatter plot.

The link is this:

https://i.imgur.com/dPeu971.gif

I'm not sure if you can view that directly, as you won't be logged in to my account, but it shows the method.  edit.  Tried it and it does load.

Please be careful copying parts of a textbook to the forum.  A while back we had a complaint from an on-line teaching company because a student had posted a worksheet.  It is a breach of copyright so we asked the student to (1) only put a single question into a request for help and (2) to type the question in their own words to avoid direct copying.  In the UK the copyright law allows copies when used for fair criticism so perhaps you could preface your post with a suitable comment such as 'This comes from <name of book> which I really like as it has good explanations and questions'

Is it Easter?  The days just blur into one what with lockdown restrictions.  Arrh! Just noticed I've got a choccy egg in front of me.  That must mean something.

Best wishes to you too.

Bob

Hello. Thank you for the tip. I will be careful not to avoid a breach of copyright.
More later....