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#376 Re: Help Me ! » Rate of Change of Linear Function » 2021-04-15 14:23:08
Other than MIF, no I don't. The Khan Academy has some U-tube videos but you cannot specify what you want to see next. Our own zetafunc has a U Tube channel that teaches some advanced topics. zetafunc might create a video for you on a topic if you ask him.
Bob
Thanks anyway. What do you think about the Photomath app?
Take a picture of any equation and ot provides a step by step solution.
Wish there was an app like Photomath for word problems.
#377 Re: Help Me ! » Rate of Change of Quadratic Function » 2021-04-14 12:21:20
Ok let's have a go. The function is f (x) = ax^2 + bx + c . If you take the general point on the curve it has coordinates
(x, ax^2 + bx + c) I'll call that point A.
We then pick a new point B that is close to A. Newton was one of two mathematicians who invented calculus. The other was Leibniz. They both came up with the idea at about the same time and a controversy raged between them about who first had the idea and whether the other 'stole' it. I'll used Newton's notation. He invented a new symbol Δx to mean 'a little bit' in the x direction. It's a single algebraic symbol not two multiplied together.
So the coordinates of B are [x + Δx, a(x + Δx)^2 + b(x+ Δx) + c] I've only used square brackets for the outer to avoid confusion with the round brackets .
So the gradient of the chord AB is
( a(x + Δx)^2 + b(x+ Δx) + c - ax^2 - bx - c) / (x + Δx - x)
Have a go at simplifying that. It will probably help if you expand the bracket (x + Δx)^2 first.
You'll find there's lots that cancels out and finally you can divide Δx into the numerator.
Bob
Cool reply. I thank you for taking the time to explain what is happening here. I will try to simplify this algebraic fraction when time allows.
Questions:
1. Are you a math professor?
2. If you are a math professor, do you teach math beyond Calculus 3 aka Vector Calculus?
3. There is a huge difference between what is called the REGULAR CALCULUS SEQUENCE (CALCULUS l, ll, and lll) and Advanced Calculus. Do you also teach Advanced Calculus? I think the course also goes by the name Tensor Calculus.
4. Are you on FB?
5. Do you have your own math website?
6. I, like most students, struggle with word problems, especially SAT, GRE and GMAT word problems. Do I plan to take the SAT, GRE AND GMAT? No. I am 56 years old but the word problems found in test prep books for the SAT, GRE AND GMAT make good practice problems. What is the best way to improve word problems skills? My greatest struggle is converting WORDS to algebraic expressions or equations.
7. Do you think it is normal for a man my age to have a passion for learning math, even though I am never going to become a math teacher?
#378 Re: Help Me ! » Rectilinear Motion » 2021-04-14 12:05:16
I've never questioned why it is called that. Hhmm! It means an object travelling along a known straight path. I googled it and was surprised to discover that linear motion means along a path that need not be straight and rectilinear means the path is straight.
In a question, if they give you the equation of motion (eg. s = 5 - t^2) then it doesn't really matter what the path is.
Bob
ps. This morning I went through all your responses and answered the ones that need an answer at this stage (I hope I didn't miss one). When I click for active posts my answered ones jump to the top of list and the ones I hadn't looked at yet stayed mixed in with the ones I'm leaving until later. So it's getting harder and harder for me to keep track of whether I've done all I need to. (hope this is making sense)
So when you are ready to return to an unanswered one from your list, please bump it back to the top by posting that you want me to deal with it. Hope that makes sense.
Hello. What's new? To respond here, I certainly would appreciate if you fully solve this problem for me. I can then use your reply to answer similar questions. My main problem is not understanding the ideas behind certain topics.
I utilize You Tube lessons, especially by Professor Leonard in my studies. He is an excellent math teacher. I am taking notes per lesson. Notes given by Professor Leonard are far easier to understand than most math textbooks. What do you think about the Math for Dummies book series?
#379 Re: Help Me ! » Approximating Velocity » 2021-04-14 11:57:24
The top table row starts with the label t and then the values 0.1, 0.01, 0.01 etc.
The second row will have the corresponding Distance (s) values calculated using the formula s = 5 - t^2
The final row will have the V values calculated using V = s / t
What you should observe is values of V getting closer and closer to a limit (the instantaneous velocity at the moment).
This process demonstrates the process known as differentiation from first principles.
Bob
Ok. I will work on creating the needed table.
#380 Re: Help Me ! » Velocity » 2021-04-14 11:55:39
Arh! Good question.
The units for V are determined by what units are used for D and T. So if you do 20/0.25 you have the velocity in ft / s.
To get an answer in mph you'll have to do the conversions.
20 ft converts to 20/(3 x 1760) miles and 0.25 s converts to 0.25/3600 hours.
Bob
Very good. Not too bad. Interesting question.
#381 Re: Help Me ! » Rate of Change of Linear Function » 2021-04-14 11:53:56
In order to keep the algebra as simple as possible, replace y1 with mx1 + c, and y2 with mx2 + c
Bob
Hello Bob. I will play with this some more. By the way, do you know if there are math websites where tutors provide a complete solution to questions (regardless of topic and level of questions) for free or for a small fee?
#382 Re: Help Me ! » Rectilinear Motion » 2021-04-12 10:30:28
I know you were advised to split your posts but all the ones you have made are related in that they form an introduction to calculus. I suggest you get the other (easier) ones sorted first; then we can proceed to the harder ones.
Bob
I will take it one at a time. What is rectilinear motion anyway?
#383 Re: Help Me ! » Approximating Velocity » 2021-04-12 10:29:03
This approach is exactly how differential calculus is developed.
The table will have a row for distance, one for time taken and one for velocity using V = D/T
Bob
Can you be more specific? I need you to further explain.
#384 Re: Help Me ! » Velocity » 2021-04-12 10:27:49
speed = distance / time
B
At a certain instant, the speedometer of an automobile
reads V mi/h. During the next 1/4 s the automobile travels 20 ft.
Estimate V from this information.
Distance = 20 feet
Time = (1/4)s
Is the formula V = 20/(1/4)s miles per hour?
#385 Re: Help Me ! » Instantaneous Rate of Change » 2021-04-12 10:24:55
I think this will have to be calculus. The other posts are an easier start so let's get them sorted first, then I'll show you this more complicated case.
Bob
Ok. Sounds good.
#386 Re: Help Me ! » Rate of Change of Linear Function » 2021-04-12 10:03:31
This also can be done using calculus or you could try this:
Write down the coordinates of two points on the line (x1,y1) and (x2,y2) and compute
difference in y coords divided by difference in x coords.
Bob
What are the specific coordinates of the two points?
#387 Re: Help Me ! » Rate of Change of Quadratic Function » 2021-04-12 10:02:23
hi
Have you met differential calculus yet?
It's here: https://www.mathsisfun.com/calculus/der … ction.html
Bob
I just started differential calculus. Can you set this one up for me?
#388 Re: Help Me ! » Find Rate of Change » 2021-04-12 10:00:21
Hello mathland,
Sorry he hear you're feeling sick. Usually it's a sign that your immune system is working so it'll most likely pass quickly. I had something similar with the astra zenica jab.
Best wishes,
Bob
Hello Bob.
How are you? I am feeling better today. It was just the reaction
of the second Moderna vaccine. Now, I can get back to my math studies.
#389 Help Me ! » Rectilinear Motion » 2021-04-11 12:48:24
- mathland
- Replies: 8
As an object in rectilinear motion moves,
its distance s from the origin at time t is given by the equation
s = s(t) = √4t, where s is in centimeters and t is in seconds.
Find the velocity v of the object at t_0 = 1 and t_0 = 4.
#390 Help Me ! » Approximating Velocity » 2021-04-11 12:46:26
- mathland
- Replies: 4
An object in rectilinear motion moves according to the equation s = 5 − t^2 (s in centimeters and t in seconds). Approximate the velocity of the object at time
t_0 = 1 by letting t first equal 0.1, then 0.01, and finally 0.001.
What limit does the velocity appear to be approaching?
Organize the results in a table.
#391 Help Me ! » Velocity » 2021-04-11 12:38:13
- mathland
- Replies: 4
At a certain instant, the speedometer of an automobile
reads V mi/h. During the next 1/4 s the automobile travels 20 ft.
Estimate V from this information.
#392 Help Me ! » Instantaneous Rate of Change » 2021-04-11 06:59:44
- mathland
- Replies: 2
The volume V of the right circular cylinder of
height 5 meters and radius r meters is given to be
V = V(r) = 5πr^2. Find the instantaneous rate of change of the
volume with respect to the radius when r = 3 meters.
I need the set up. Thanks.
#393 Help Me ! » Rate of Change of Linear Function » 2021-04-11 06:54:54
- mathland
- Replies: 6
Show that the rate of change of a linear
function f (x) = mx + b is the slope m of the line y = mx + b.
Can someone get me started here?
#394 Help Me ! » Rate of Change of Quadratic Function » 2021-04-11 06:22:15
- mathland
- Replies: 8
Show that the rate of change of a quadratic
function f (x) = ax^2 + bx + c is a linear function of x.
Can someone get me started here?
#395 Re: Help Me ! » Find Rate of Change » 2021-04-11 01:56:01
hi mathland,
If you can use algebra to get a (x-c) term at the top of that expression, then these can be cancelled out and what's left will allow you to let x tend to c.
Now you can cancel the (x-c) and simplify the rest, put x=c and you're done.
Bob
Hello Bob. How are you? I took my second vaccine of Moderna yesterday and feel sick today. Everyone told me to expect getting sick the next day. They were right in this respect. I thank for you for using algebra to simplify the original set up.
I can take it from here. No math today. Just not feeling myself. This forum is ok. I would like to see more people involved. It's good to see others participate in the Help Me forum. It's always the same people.
#396 Help Me ! » Find Rate of Change » 2021-04-10 04:14:34
- mathland
- Replies: 4
Find the rate of change of the function at any number c.
f(x) = x^2/(x + 3) as x tends to c.
I need to find the limit of [f(x) - f(c)]/(x - c) as x tends to c.
lim......[(x^2)/(x + 3) - (c^2)/(c + 3)] /(x - c)
x-->c
Stuck here.
#397 Re: Help Me ! » Epsilon-delta Limit Proof » 2021-04-06 10:07:26
hi mathland,
This is not a topic I have worked on before, so I've waited a while in the hope someone else might give an answer.
As that hasn't happened yet I've started by researching the method. I found this pdf which I found very clear.
https://math.berkeley.edu/~willij/1a/epsilonics.pdf
Then I did the following. You'll have to decide if it is a proper solution:
As x is close to 1 we may assume that 3-x > 0 therefore
So for any epsilon I have found an epsilon dependant delta . I think that is what the method requires.
Let me know what you think.
Bob
Hello Bob. Thanks for the link and effort. The proof is more intense, more rigorous than your reply. I posted the problem at another forum. Someone was kind enough to work out the entire proof.
Scary stuff. Thank God I am NOT taking Calculus 1 in a classroom setting. I like the epsilon-delta proof but it just hasn't sinked deep enough for me to feel comfortable solving problems.
#398 Re: Help Me ! » Limit of Rational Function...2 » 2021-04-05 01:18:46
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....
#399 Help Me ! » Epsilon-delta Limit Proof » 2021-04-05 01:14:02
- mathland
- Replies: 2
Use the epsilon-delta method to show that the limit is 3/2 for the given function.
lim (1 + 2x)/(3 - x) = 3/2
x-->1
I want to find a delta so that | x - 1| < delta implies |f(x) - L| < epsilon.
| (1 + 2x)/(3 - x) - (3/2) | < epsilon
-epsilon < (1 + 2x)/(3 - x) - 3/2 < epsilon
I now add 3/2 to all terms.
(3/2) - epsilon < (1 + 2x)/(3 - x) < (3/2) + epsilon
Stuck here....
#400 Re: Help Me ! » Limit of Rational Function...3 » 2021-04-03 23:57:26
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............1249.68I 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?