Calculus I and III -- problems and suggestions' Journal|
[Most Recent Entries]
Below are the 12 most recent journal entries recorded in
Calculus I and III -- problems and suggestions' LiveJournal:
|Saturday, February 3rd, 2007|
Limits involving infinity and asymptotes, with trig functions
I am a Calculus I student just starting out.
I understand (I think) the concept of limit, which we started with.
Now, though, we're doing limits involving infinity, and I'm starting to get confused.
I can handle finding vertical and horizontal asymptotes of regular rational functions, but when they start throwing natural logs and trig functions in there, I'm getting lost.
In this problem I am supposed to find vertical asymptotes, if any; the behavior of the graph on each side of each vertical asymptote; and the horizontal asymptotes, if any.
The problem: f(x) = 4 tan -1
Now, my thinking is that, since the graph of the inverse tangent is continuous on all x, then the graph of inverse tangent multiplied by four and then subtracting one is continuous on all x. That seems to be correct, as far as the answer in my book is concerned; I was thinking there would be no vertical asymptotes, and the book agrees.
However, when it comes to horizontal asymptotes, I get confused. On this problem, I was thinking that, as x approaches infinity, the inverse tangent of x would approach 1, so the limit was 3. As x approaches negative infinity, the inverse tangent of x would approach -1, so the limit was -5. Therefore, I thought that the horizontal asymptotes would be where f(x) = -5 and 3. The book, though, gives the answer as +/- 2(pi) - 1.
Can anybody help explain any of this? Sorry if I'm not being too clear about what I don't understand. I'm so confused at this point that I'm not even really sure what it is that I'm confused about. Thank you!
|Tuesday, October 3rd, 2006|
Hi, a noobie here. I got an assignment a few days ago (that's due end of tomorrow), and I managed to complete most of it, but I have three questions in the "difficult" section that I can't solve. I missed a couple of classes so I sort of taught myself what I know from the textbook. The other questions were fine, since they were modeled after the textbook questions, but these three aren't, so, uhm, help, please~
1) log(base 2)x + log(base 4)x + log(base 8)x = 33
So far, I isolate the terms with x to one side, then use log laws to express each side, and try to simplify, then check my answers, but I don't see a single example in my textbook with logs with different bases.
2) explain why there are no solutions to the equation log: log(base 5)(-125) = x and log(base -2)16=x
I'm pretty sure the answer is just that when you find the roots and test the equation, the answer is less than zero, and since x can't be less than zero, the logs don't check out. But how I prove it, I have NO CLUE.
3) log(base 5)(log(base4)(log(base3)x)) = 1
...I see the different bases, and I'm completely lost.
Could someone please show me how it works? I'd like to know the steps, so when I see this on a test I'll know what to do)
Normally, I would have went to extra help, but I can't because the teacher is away at BAND CAMP. She's back after I hand my assignment in. Sigh. Thanks in advance!
|Monday, June 26th, 2006|
If anyone can help me, it would be appreciated greatly. I'm taking AP Calc and some of the summer work is getting to me.
(-8ab)((2/a-2/b) / (a-b))
(x^2+4x+3/x^2-1) / (x^2+x-6/x^2+3x-10)
|Tuesday, November 29th, 2005|
oh my lord. please be someone alive out there:
determine the values of a, b and c when:
y=18x-27 is the slope of the tangent at (3,27)
and (-1.5,0) is the P.O.I.
|Sunday, November 20th, 2005|
i was wondering if anyone can show me how to graph part c) photoshop or paint is fine. because i don't kno if i did this graph right or not? ( clickCollapse ) Current Mood: hopeful
|Wednesday, November 9th, 2005|
Im in Calc 1 and only know the Derivatives, Limits, and the MVT.
I need help with this problem.
A metal gutter is to have 10cm sides and a 12cm horizontal bottom, with the sides making equal angles with the bottom. How wide should the opening across the top be so that the gutter would have maximum carrying capacity? (Obviously the gutter is to make a Trapezoid.) Current Mood: anxious
|Sunday, October 23rd, 2005|
Does anyone know how to get from
? Where g(x) is an arbitrary continuous function. It's really bugging me...
I think it has something to do with splitting iterated integrals.
|Tuesday, August 9th, 2005|
Hi, I'm new.
I just took Calculus I over the summer, and I'll be taking Calc AB in the fall because my school is crazy and said Calc BC didn't fit. Oh well. When school starts again I'll probably post more. See you then!
|Saturday, January 29th, 2005|
i was given sine graph :y=2sin(3t-(pi/4))+8 adn then i was told to use CALCULUS to work out the value of y when t=0.2
i know that i can work out the instantaneous rate of change at that point by using drawing the graph adn then another tangent at t =0.2, but i was just wondering how am i menat to use CALCULUS to solve this problem
if anybody does know then i would really really appreciate it if u could leave a little comment...thnxs pplz
|Friday, October 8th, 2004|
062 - Project 2
Well... Any suggestions for the next one? This one was supposed to leave you some room for "creativity" -- did it overdo it? Are the questions clear? I need some feedback, people. Otherwise it will be the same thing again in a couple of weeks :-)
Project -- 060
How did you think project 2 went? Too short? Too long? Not enough open-ended questions?
|Tuesday, September 28th, 2004|
Please post your comments and suggestions here. Try to be constructive and specific, for example : the last project was awful because (list of things you didn't like) and it would really help me if (suggestions on improvement). Thanks guys!