[princeclassic]

ok, so i've got an exam in a few days and their are a couple practice problems that me and my roommate are really struggling with.

1. derivative of [(1+x^2)^inverse tan(x)]

2. intergral from 0 to 1 of (2x+1)/(x^2+1)

3. simplify sec(inverse cot(2x)) [the answer should be in terms of x...no trig functions]

any help is greatly appreciated...

 

[psxguy85]

Solution to #2:

I separated the integrals into int (2x/(x^2 +1)) and int (1/(x^2+1)) I left out the limits until the end.

The second integral is easy, if you look at the inverse trig formulas thats just inverse tan and the first integral is done by doing a u substitution on the (x^2+1). The solution to the integration without the limits is ln(x^2 +1) + inverse tan x, and then put that through the limits.

The answer is ln 2 + pie/4.

Solution to #3:

I just did a triangle and figured out what the inverse cotangent of 2x looks like on a triangle. Just do the a^2+b^2 = c^2 rule to figure out what C is, which is the hypotenuse. Take the secant of that same angle on the triangle (hypotenuse/adjacent) and the answer is root(4x^2 + 1)/(2x)

I'm still working on the first one, but it involves implicit differentiation to let you know. You have to do a log function to get the inverse tan in front of the 1+x^2 but then you have to differentiate the y side as well. Hope this helps some.

 

[Born2bwire]

Damn... I haven't done anything like this since high school. All my Calc stuff is multivar, vector, or along the lines of Greens and Stokes.

 

[gpalmer]

Quote:

Originally posted by psxguy85 You have to do a log function to get the inverse tan in front of the 1+x^2 but then you have to differentiate the y side as well. Hope this helps some.

Are you sure that one isn't actually a substitution of arc sins and cosines in place of the arc tangent? It's been too long since I did my math, I would have to think and I don't wanna!

 

[psxguy85]

Quote:

Originally posted by gpalmer Are you sure that one isn't actually a substitution of arc sins and cosines in place of the arc tangent? It's been too long since I did my math, I would have to think and I don't wanna!

I dunno, its just a suggestion I am giving, I don't know how to do it and thats why I didn't put a solution down.

 

[princeclassic]

thanks so much psxguy!!

 

[hop ham]

1.

[ln((x^2)+1)/((x^2)+1) + (2*x*invtan(x))/((x^2)+1)] *((x^2)+1) ^invtan(x)



TI89 skills

 

[Iron_Dreamer]

Quote:

Originally posted by hop ham TI89 skills

Hehe, I sure know that line all too well

 

[hop ham]

when i was a ugrad at rutgers, i would carry my 89 in my pocket...an engineer can't leave home without it

i know, i know...what a sad pathetic life...yes, it was.

 

[psxguy85]

Quote:

Originally posted by hop ham 1. [ln((x^2)+1)/((x^2)+1) + (2*x*invtan(x))/((x^2)+1)] *((x^2)+1) ^invtan(x) TI89 skills

Good times. I figured out how to do that without the calculator, you do have to do implicit differentiation. That is what you get with the calculator ti-89 though. I'm not allowed to use ti-89 on my exams. SIGH!

 

[bralack42]

A great website for derivatives can be found at calc101.com. Is this the same thing the TI-89 can do?

 

[ECM]

Hop Ham, an engineer with a TI89?? cmon....I thought ALL engineers used HP48GX's. I'm not an engineer, but a physics undergrad and that RPN sure comes in handy!!

 

[Born2bwire]

Quote:

Originally posted by ECM Hop Ham, an engineer with a TI89?? cmon....I thought ALL engineers used HP48GX's. I'm not an engineer, but a physics undergrad and that RPN sure comes in handy!!

I don't know anyone that uses an HP. I use an 86 though, there's something satisfying about working it out by hand (ok, maybe I spent all my calculator money on tubes).

 

[Harrath]

This handy thing saved my life in Calculus:

http://integrals.wolfram.com/index.en.cgi

 

[ADS]

Quote:

Originally posted by Born2bwire I don't know anyone that uses an HP. I use an 86 though, there's something satisfying about working it out by hand (ok, maybe I spent all my calculator money on tubes).

The HP48 is an engineer's dream. Believe me, I've used it instead of my TI89 for every class I've taken, and it has performed wonderfully. (I'm a computer engineering student) I'm surprised you haven't seen anyone using one.