We finished the exploration 4-2 on Friday. So basically we just checked our answers with Bru.
Firstly, let’s review the Quotient Rule!!!
I think this image just concludes the Quotient Rule. It is pretty straightforward.
Secondly, let’s take a look at the “Your Understanding” part of the package of the Quotient Rule. We went over this part of the package smoothly. The only issue we had was about question 3. In the “In words” part of part e, “As x gets arbitrarily close to 1, the function h(x) gets arbitrarily far from 0”, some people thought that instead of “far from 0” it should be far from 1, since (1,1) is the midpoint of the whole graph. Bru said both 0 and 1 works.
So now let’s turn the page over to Exercises. The 4 questions we talked about in the class are question 2, 4, 5 and 6. You can check the details in the slide show which Bru had posted two days ago. One reminder: Be aware of the composite functions. Don't forget the Chain Rule. Here I will just provide you the answers for the other 2 questions.
1. f '(x) = {(4x^3) * cosx - (x^4) *(- sinx)}/(cosx)^2
= x^3 (cosx + xsinx)/(cosx)^2
3. f '(x) = {(5cos5x)(8x-3) - 8sin5x}/(8x-3)^2
= {(40xcos5x-15cos5x-8sin5x}/(8x-3)^2
If you guys have any questions about my answers, please leave a comment.
Finally, I ask you guys to check out this YouTube clip.
http://www.youtube.com/watch?v=K3MxofAF-9o
This guy is left handed. I believe this YouTube clip will teach you the Quotient Rule again.
By the way, there are some extra credits. Check this link. You will see the problems.
https://docs.google.com/a/crms.org/viewer?a=v&pid=sites&srcid=Y3Jtcy5vcmd8Y2FsY3VsdXN8Z3g6NDMwNzcwYmY2ZTQ2MjE4Mg
There is a quiz on Monday about both Product Rule and Quotient Rule. Be Ready for that.
I feel there is nothing more to say.
So BlueElephant, you are up again.
Feel Free to live any comments!!
Posts
I think there is a small error in your answer to #1. I put {(4x^3)*cosx+(x^4)*(sinx)}/(cosx)^2. Notice that there is no negative sign in front of the (sinx) in the second term. While the derivative of (cosx) is (-sinx), according to the quotient rule, the terms are separated by a subtraction sign. When simplifying the equation, I changed the subtraction sign to an addition sign and made the (-sinx) positive. If you were to leave (-sinx) as it is, you would have to leave the subtraction sign in between the two terms.
ReplyDeleteGreat and complete post. I was a little confused with how the numbers '2,' '3' and '1' in the first image above the arrows play into the image. Would you please explain that to me? I also think it might have been beneficial to post the answers to the rest of the questions that we went over in class for the numerous students who were absent. In the future, your post could be a little more clear if you used equation editor. But other than that, great video post (although a bit long) and very complete lesson
ReplyDeletesecret,
ReplyDeleteThanks for pointing that out. I am wrong.
Dammitimmad,
I think the numbers 1, 2, and 3 are just marking the steps you need to take to complete the quotient rule. I tried to use the equation editor thing, but I could not get what I really wanted. I will practice to use the equation editor and do it next time. Thank you!
Overall good job, however it may be a bit short, you could have restated somethings from the other day just as a bit of help. I thought that the graphic you found was awesome though, really helpful so thanks for that.
ReplyDeleteI thought that this site was really helpful maybe you guys will too.
http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/quotientruledirectory/QuotientRule.html
Hi YDPLUSSB,
ReplyDeleteI thought the length of this post was great! I really think it is a great skill to be able to get in all of the information necessary in a short and sweet, yet concise, scribe post. Besides the previous recommendation to keep up the practice on equation editor for future posts, I have only one more small recommendation. Because these problems have multiple steps and often multiple ways in which to solve/simplify them I think it would be beneficial to show the steps that you did to find the answer. I know that showing all the steps would probably double the amount of time that it takes to create this scribe post, so maybe just show all the steps for anywhere from one to a few problems. This would also help reinforce the quotient rule in everyone's mind.
Thanks and good job!
mc Casper
Like Mc Casper I think that the length of this post was great, there was not that much to cover, and when a post is brief I can enjoy the process more, once they get too long I start to tune out. One suggestion for the future is that instead of posting the whole link at the end of your post you could use a hyperlink that would make it easier for the reader, clutter can sometimes distract from the point of the post. And at a first glance I was confused by the picture because I'm not sure we went over it in class. But overall I enjoyed reading your post, thanks!
ReplyDeleteThe picture was a bit confusing to me at first, but I understand it now. I think it would have been helpful to have a verbal definition of the quotient rule in addition to that picture. Thank you for the good examples. Also, I liked the Youtube video, and thanks especially for the reminder about the quiz. Overall, this was a helpful review of the Quotient Rule.
ReplyDelete