User not logged in - login - register
Home Calendar Books School Tool Photo Gallery Message Boards Users Statistics Advertise Site Info
go to bottom | |
 Message Boards » » Calc Tutoring is here - Try it for free! Page [1]  
jobarc
New Recruit
7 Posts
user info
edit post

Are you having trouble with your math class?
Problem solved!

Private tutoring sessions with someone who speaks to your common sense.

Experienced tutor for all Calculus and precalculus.

See how simple it is to make it through Calculus.

First half of the first hour is free!
So first hour is only $10

$20 per any additional hour

email to schedule an appointment - zliran@ncsu.edu
or just call - 919-7605579

Schedule is limited so hurry up to get your time slot.


[Edited on September 24, 2007 at 6:43 PM. Reason : .]

9/24/2007 6:19:07 PM

Ernie
All American
45943 Posts
user info
edit post

your last name is iran?

9/24/2007 6:29:22 PM

jobarc
New Recruit
7 Posts
user info
edit post

it's Liran... Iran would be kinda freaky.... don't you think?

9/24/2007 6:35:00 PM

mathman
All American
1631 Posts
user info
edit post

first you must prove your worth. We'll start out easy,

Int ( x / (x-1) )dx

9/24/2007 9:23:24 PM

jobarc
New Recruit
7 Posts
user info
edit post

you have the number and you have the email.
I'll show you a few ways to approach the problem.
feel free to contact

9/25/2007 10:42:32 AM

rainman
Veteran
358 Posts
user info
edit post

Its a scam if he can't answer that.

9/25/2007 11:18:17 AM

LimpyNuts
All American
16859 Posts
user info
edit post

Quote :
"first you must prove your worth. We'll start out easy,

Int ( x / (x-1) )dx"

um... (x-1) + ln(abs(x-1)) + "C"

[Edited on September 25, 2007 at 4:36 PM. Reason : +C]

9/25/2007 4:36:04 PM

Jrb599
All American
8846 Posts
user info
edit post

^WRONG!

x + ln(x-1)

9/25/2007 6:52:24 PM

LimpyNuts
All American
16859 Posts
user info
edit post

it's entirely correct. the substitution i used produces (x-1), however, that -1 can be assigned to part of the "C" constant yielding:

x + ln(abs(x-1)) + "C"

and yes, the absolute value DOES belong there

9/25/2007 9:19:06 PM

AntecK7
All American
7755 Posts
user info
edit post

Yea i dont htink you can do it without the abs.

9/25/2007 9:32:39 PM

mathman
All American
1631 Posts
user info
edit post

ha, if you were a good tutor you would have already answered the question. See even TWW is better for free!

9/25/2007 10:07:57 PM

mathman
All American
1631 Posts
user info
edit post

To be fair I'll give you another chance, this time we adjust the level of skill needed, level up as it were,

Int ( sec(x) dx )

good luck to you sir.

9/25/2007 11:42:03 PM

LimpyNuts
All American
16859 Posts
user info
edit post

how is this one any harder?


By the way, I'll tutor calculus 1, 2, 3, differential equations, statisticsor just about any other undergraduate level applied math course (no number theory) in exchange for lunch.

[Edited on September 26, 2007 at 12:34 AM. Reason : -]

9/26/2007 12:21:42 AM

joe_schmoe
All American
18758 Posts
user info
edit post

ln (abs (sec x + tan x)) + C

TI-89 FTW




[Edited on September 26, 2007 at 1:13 AM. Reason : ]

9/26/2007 1:11:04 AM

Jrb599
All American
8846 Posts
user info
edit post

Quote :
"it's entirely correct. the substitution i used produces (x-1), however, that -1 can be assigned to part of the "C" constant yielding:"


I shoulda rephrased, yes it's right, but we all know 99.9% of calc teachers would of marked something off.

[Edited on September 26, 2007 at 7:46 AM. Reason : ]

9/26/2007 7:45:48 AM

clalias
All American
1580 Posts
user info
edit post

Would have marked wrong on your answer.

9/26/2007 8:28:08 AM

LimpyNuts
All American
16859 Posts
user info
edit post

^^ your answer on the other hand was ACTUALLY wrong

9/26/2007 4:19:15 PM

Jrb599
All American
8846 Posts
user info
edit post

yeah I know I didn't put +C or abs value, blah blah blah.

9/26/2007 5:44:57 PM

joe_schmoe
All American
18758 Posts
user info
edit post

those abs value bars are basically junk anyhow.

they just |clutterin| up |shit|

who needs em?

9/26/2007 7:23:02 PM

mathman
All American
1631 Posts
user info
edit post

joe_schmoe, hey, calculators are cheating.

Of course the TI-89 can do much more than most of us.

LimpyNuts you think the integral of sec(x) is not much harder than
the integral of x/(x-1) ? How would you do the integral of sec(x) ?
As far as I know sec(x) is not that easy w/o a trick.
x/(x-1) on the other hand is like 2 lines.

anyway apparently jobarc does not have the goods.

9/26/2007 7:28:09 PM

mathman
All American
1631 Posts
user info
edit post

^^ integrate 1/x from -5 to -3 w/o the absolute value bars, see how that goes for you.

9/26/2007 7:29:13 PM

joe_schmoe
All American
18758 Posts
user info
edit post

it's a joke son, a joke Ah say!





(* i think it's too quick for him *)

9/26/2007 7:53:32 PM

LimpyNuts
All American
16859 Posts
user info
edit post

Quote :
"LimpyNuts you think the integral of sec(x) is not much harder than
the integral of x/(x-1) ? How would you do the integral of sec(x) ?
As far as I know sec(x) is not that easy w/o a trick.
x/(x-1) on the other hand is like 2 lines."


sec(x)*(sec(x)+tan(x))/(sec(x)+tan(x)) dx = dY/Y where Y = sec(x)+tan(x)
... ---> ln(abs(sec(x)+tan(x)))

you can do it in your head... all it requires is that you know what the derivative of sec(x) is.

9/26/2007 9:08:51 PM

mathman
All American
1631 Posts
user info
edit post

^yeah that's the trick, where did you learn it ?
That integral is like a half-page w/o that very nonintuitive substitution.

and to joe_schmoe I knew you were joking, just speaking to the abs-value haters out there.

9/26/2007 9:47:34 PM

joe_schmoe
All American
18758 Posts
user info
edit post

9/26/2007 10:09:50 PM

LimpyNuts
All American
16859 Posts
user info
edit post

^^ i didn't learn the "trick" anywhere. it was pretty apparent to me. of course after you're given the answer taking the derivative gives you the expression.

9/26/2007 10:14:41 PM

mathman
All American
1631 Posts
user info
edit post

seriously, you just look at Int( sec(x)dx ) and think well maybe I should try Y = sec(x) + tan(x) ?

That's obvious ?

That's what I teach my students, but I doubt anybody would dream that up w/o some help.

If you did then I'm impressed, seriously.

To compare, something like Int( x*exp(x^2) dx ) just screams u = x^2 in your face.

The question is why try Y= sec(x) + tan(x) ?

The answer "it works" is insufficient.

[Edited on September 27, 2007 at 12:00 AM. Reason : .]

9/26/2007 11:58:10 PM

LimpyNuts
All American
16859 Posts
user info
edit post

My line of thought:

hmm.. trig substitution?
*thinks about triangles for a second*
no...
well d(tan(x))=sec^2(x)
what's the derivative of sec(x) again? oh yeah sec(x)*tan(x)
*click*
sec(x)*(sec(x)+tan(x)) = d(sec(x)+tan(x))/dx


maybe i'm just special? when i seen an integral that isn't obvious i just start trying to work backwards. it usually works for integrals with simple expressions. but once you know the trick you can get:

int(csc(x)) = -ln(abs(csc(x)+cot(x))) ----- d(csc(x)) = csc(x)cot(x)
int(tan(x)) = -ln(abs(cos(x)) ... etc.
int(cot(x)) = ln(sin(x))

9/27/2007 1:31:47 AM

mathman
All American
1631 Posts
user info
edit post

^ nice way of thinking. But, are you using the answer to guess the u-sub. ?
Interesting idea. I learned the trick from a friend. We didn't do that sort of thing in my calc II so I only learned of it when I started teaching.

9/27/2007 11:15:50 PM

LimpyNuts
All American
16859 Posts
user info
edit post

for the sec(x) problem i didn't know the answer before i figured out how to get it. what i meant was that i applied the same thought process to obtain the other 3 integrals, which are also not immediately apparent.

9/28/2007 12:15:18 AM

mathman
All American
1631 Posts
user info
edit post

Nice work indeed.^

Let me see if I can come up with something a little harder,

Int ( 1 / [1 + sin(x) + 2*cos(x) ] )dx

Or to make it more fun,

Int ( [ A*cos(x) + B*sin(x) + C ] / [ D*cos(x) + E*sin(x) + F ] )dx

for arbitrary, but sensible, constants A,B,C,D,E,F.

9/28/2007 12:58:31 AM

LimpyNuts
All American
16859 Posts
user info
edit post

^not difficult, per se, but extremely time consuming.

inverse tangents, FTL

9/30/2007 7:03:20 PM

mathman
All American
1631 Posts
user info
edit post

something like that, but I don't think I'd classify it not difficult.

What do you consider difficult integration?

btw the silence of jobarc is deafening.

9/30/2007 7:29:52 PM

DannyBoy
All American
883 Posts
user info
edit post

well this thread failed

9/30/2007 7:41:08 PM

LimpyNuts
All American
16859 Posts
user info
edit post

^^ difficult in this context would be something that the average person (of the intended audience... i.e. calculus tutors) would not recognize how to solve immediately.

That said, I would say the previous problem and the sec(x) problem are of moderate difficulty. ln(cosh(x)), for example could be considered very difficult. While I know it has an answer, I've never been able to attain it.

9/30/2007 9:59:44 PM

mathman
All American
1631 Posts
user info
edit post

^^ no the thread fails you.
^ hmm... interesting. I'll ask my math muse later.

9/30/2007 10:49:13 PM

NukeWolf
All American
1232 Posts
user info
edit post

The only simple method for Int(ln(cosh(x)) would be to cheat and go here:

http://integrals.wolfram.com/index.jsp

The result is certianly non-obvious. My gut feeling is to expand everything in terms of taylor series and integrate term by term. You could at least get an approximate solution. If you guys can think of a more elegant way, please share. I never did take functional analysis.

10/1/2007 10:24:06 AM

clalias
All American
1580 Posts
user info
edit post

you wouldn't learn that in functional analysis anyway.

10/1/2007 11:47:59 AM

mathman
All American
1631 Posts
user info
edit post

^^ hmm... polylogarithms... this is a special functions problem then. So your gut feeling is probably spot on, I've still got a lot to learn about special functions myself.

Seeing ln(cosh(x)) makes me think some sort of ma 513 trickery may help. But the poylog's in the answer tell me it's above my current skill level.

^ yeah really. You don't really learn how to calculate anything in functional analysis. Unless you count
calculating the norm of an infinite dimensional vector, ok I guess that's something. Anyway, functional analysis is really about learning how to avoid the paradoxes the can arise from sloppy math-think.

10/1/2007 1:15:53 PM

 Message Boards » Study Hall » Calc Tutoring is here - Try it for free! Page [1]  
go to top | |
Admin Options : move topic | lock topic

© 2024 by The Wolf Web - All Rights Reserved.
The material located at this site is not endorsed, sponsored or provided by or on behalf of North Carolina State University.
Powered by CrazyWeb v2.39 - our disclaimer.