Need help with calculus

[Maleficus]

Ok well here i am day before the test trying to learn my calculus because i have an incredibly hard time learning/paying attention to my teacher.

I really need someones help explaining this to me.

If someone will lend me some webspace i have a scan of the review of the material i will be tested over until then i will give you one problem of each and maybe you guys can help me learn this.


Find the derivative of the functions

Y = cos2x * ln 3x^2

Find the equation of the tangent line to the equation

Y = (ln x)/X^2 at the point (1,0)

Evaluate the integrals

Sin x/(1+cosx) dx

TIA

 

[tallest1]

Hints:

1) Use the product rule

2) Find the derivitive of Y, plug in the X value, and kablam, you got the slope of the equation

3) Use substitution (changing from DX to DY, etc), though that may be a calc 2 concept. I forget

 

[silverpig]

1)

y = cos2x*ln3x^2

let u = cos2x
u' = -2sinx

let v = ln3x^2
v' = 1/3x^2 * 6x = x/2

y' = u'v + uv'

y' = -2sinx*ln3x^2 + cos2x*x/2

2) Take the derivative of the function. Plug in the point (1,0) to find the slope at (1,0). You now have a slope, and a point. Use (y-yo)=m(x-xo), where yo = 0, xo = 1, and m is what you just found.

3)

let u = (1+cosx)
du = -sinx dx
-du = sinx dx

The integral becomes int(-du/u) = -ln u

sub for u again, you get -ln(1 + cosx)


*disclaimer* did this off the top of my head, and I've got a major headache right now.

 

[silverpig]

Previous message edited for negative sign error...

 

[NozlerAtClemson]

not that it will help you but I know how you feel. last semester I took calc III from a lady how was supposedly speaking english but it didn't sound that way to me. Heavy chinese accent+female high picth voice+me having some loss of hearing in the upper freq. = didn't pass calc.

 

[CSoup]

What is calc III? My school only had two semesters of Engineering Calculus. The only book ever used for calc was the blue or purple Thomas and Finney multivariable calc book and we covered all chapters in it.

I hope I did not miss out on stuff I am supposed to know as an engineer.

 

[yomega]

<< What is calc III? My school only had two semesters of Engineering Calculus. The only book ever used for calc was the blue or purple Thomas and Finney multivariable calc book and we covered all chapters in it.

I hope I did not miss out on stuff I am supposed to know as an engineer. >>




Calc III is all vector stuff, vector field and such, and you will not probably not need it as an engineer.

EDIT: also if you took engineering calculus then they may have covered it and skipped some useless stuff.

 

[silverpig]

Calc III is multivariable calculus. 3 and 4 (and higher) dimensional calculus, surfaces, volumes... etc. There's a bit of an intro into vector calculus too, which is yet another course.

 

[yomega]

the calc 3 curriculum varies alot between schools, some schools have almost no vector stuff, while some have almost all vector.

 

[Maleficus]

ok thats nice about calc 3 guys but i still have no idea what im doing and silverpig thanks for trying but im still lost when i try adn do it on my own

 

[railer]

Uh...you guys are in college I hope. I can't imagine an engineering student not taking any calc above calc II. That's scary....

 

[CSoup]

<< Uh...you guys are in college I hope. I can't imagine an engineering student not taking any calc above calc II. That's scary.... >>



Hmm. This is scaring me also. We only had two semesters of calc at my engineering school (4 credits each). I paid a ton to go there also, so I hope I am not missing something very fundamental.

 

[Maleficus]

I'm a junior in highschool... anyway i need helpz plz!!!!!

 

[yomega]

Well I'm a Comp Engineering Sophmore, and I'm taking Diff Eq right now.

Maleficus, I'd be willing to help, but you need to ask a more direct question, in what part in silverpigs explination are you getting lost?

 

[silverpig]

What part are you having trouble with? What can you get on your own, and where to you get stuck?

 

[Maleficus]

i can understand how you are doing it but i am having trouble applying it on my own

like on this problem i have the work and the answer in front of me but i cant do it on my own


(ln sqrt x) / x dx

Evaluate the Integral

 

[silverpig]

General strategy for evaluating integrals of two functions in a quotient: Do a substitution. Try and make that ln(sqrt(x)) into something easy, like ln (u). Then just follow the normal substitution method. It involves a bit of guess work sometimes, but just keep trying things, and you'll eventually get to an easy integral.

 

[silverpig]

Oh, also don't worry if you do poorly on this test, and if you don't get this stuff right away. When I did my first calc class, I was getting 60-70% on most things (as opposed to 95%+ in honours math). I had a test on implicit differentiation which I failed. I then asked another teacher for a bit of help (it's good to get a different point of view on things sometimes), and I re-wrote the test (different version of course). My 40% in 2 hours was replaced with a 100% in 35 minutes. After that, it all just came to me, and I got 95% on everything else. It just takes a while to get used to it, but once you do, it's simple really...

 

[hwstock]

<< i can understand how you are doing it but i am having trouble applying it on my own

like on this problem i have the work and the answer in front of me but i cant do it on my own

(ln sqrt x) / x dx
Evaluate the Integral >>



They are expecting you to look for patterns, to use tricks. There is nothing wrong with breaking it into two substitutions. In this case, they want you to get it into a form like
A*ln(u) *(du/u) , since du/u = d(ln(u)). At that point, the answer wil be staring you in the face.

It's like doing crossword puzzles; after a while, you recognize the tricks, but in the meantime you leave a lot of puzzles unfinished. The guys who write the textbooks like to give people problems that have shortcuts, to see if they recognize the shortcuts... or if instead, they flail away trying to do integration by parts, etc.

 

[Bluga]

<< What is calc III? My school only had two semesters of Engineering Calculus. The only book ever used for calc was the blue or purple Thomas and Finney multivariable calc book and we covered all chapters in it. >>



although i'm in EE, we used Salas's book (for mathematicians). Tough, especially CalII, where triple integral, divergence, stoke's came into play.