Calculus Geniuses Needed

[MofletaLTD]

Well, not really geniuses, just those with good memory

I'm so sick of trying to remember how to do these that I'm getting a headache (I took this class about two years ago)
anyway:
Problems

Any way you can do these would help, and if you can show the way in which you did them it will help a lot.

Thank you in advance

Edit:
BTW: Not homework in case ur wondering, a friend of mine started crying that he can't do math so I helped him with everything, I just can't get these two to look right for some reason.
And its not really against the rules of the forum, so what the heck...I figured I'll ask for your help.

 

[pnb263]

ouch... I graduated as an EE, and almost received a major in math for the number of courses I took of it. I graduated about 3 years ago, and looking at that problem, my brain started to hurt. Ill get back to you on that one...

 

[TuxDave]

For the second one, can't you solve by direct substitution?

lim sin(cos(0))*cos(0) = sin(1)*1?

 

[itachi]

x=sqrt(x*tan(x/y=Z))
ln x = 0.5 ln x + 0.5 ln tan Z
0.5 ln x = 0.5 ln tan Z
1/x = (sec^2 Z / tan Z) dZ
1/dZ = x * (sin Z cos Z)
dy/dx = x * sin Z cos Z

..half-asleep.. might be wrong.

 

[MofletaLTD]

Originally posted by: pnb263
ouch... I graduated as an EE, and almost received a major in math for the number of courses I took of it. I graduated about 3 years ago, and looking at that problem, my brain started to hurt. Ill get back to you on that one...

Sounds like you know how I feel

Originally posted by: TuxDave
For the second one, can't you solve by direct substitution?

lim sin(cos(0))*cos(0) = sin(1)*1?

I really thought about that..but then I thought, what? sin of 1 radian? it makes no sence or it makes complete sence...I just can't figure it out.
Thank you though

Originally posted by: itachi
x=sqrt(x*tan(x/y=Z))
ln x = 0.5 ln x + 0.5 ln tan Z
0.5 ln x = 0.5 ln tan Z
1/x = (sec^2 Z / tan Z) dZ
1/dZ = x * (sin Z cos Z)
dy/dx = x * sin Z cos Z

..half-asleep.. might be wrong.

I wish I understood where were you going with the natural log
the kid didn't even learn those, he looked at me with owe for a minute there
Thank you for trying

 

[User1001]

link not working for me

 

[User1001]

3b is l'hopital's rule with indeterminate form 0/0 so you just take the derivative of the numerator and denomenator separately and plugin (do this twice) and then put it back as a fraction and plugin.

 

[User1001]

2) is implicit differention with annoying chain rules
d/dx x = d/dx (x*tan(x/y))^(1/2)
1=.5(x*tan(y/x))^(-1/2)*(tan(x/y)+x*sec(x/y)^2*-y^(-2)*dy/dx)
then solve for dy/dx
(I think I did it right)

 

[User1001]

3a) Simple rearrange and plug and chug
Sin(cos x)/secx=sin(cos x)*cosx
Lim as x->0 sin(cos(0))*cos(0)=Sin(1)*Cos(0)=1*Sin(1)=sin(1)=.841....

 

[coomar]

first year calc is so tedious

 

[MofletaLTD]

Originally posted by: coomar
first year calc is so tedious

and if you already passed it...its practically impossible to go back...I hope nobody ever comes to me with more calc

User1001: Hmmm...you were on the right track with number 2 but you kinda did the derivative wrong
3a) completely like me, I hope its right..
b) don't know that rule, and there are no derivatives involved in just limits (as far as I know)
Thanks for trying to help

 

[coomar]

you do use l'hospital for the last one

3b) of form 0/0

f(x)=sin^2(x)*(3x)
g(x)=x^2

f'(x)=2sinx*cosx*3x+3sin^2(x)
g'(x)=2x

seperate, divide out x and use 2sinxcosx=2sin2x

your left with 3sin^2(x)/2x which is of form 0/0 use l'hospital

6sinx*cosx/2=0

 

[magomago]

yeah seems u guys got the solved...but for some reason i can do stuff like laplace without a problem, or i can can bust out vector calculcus..bit i get lost on this

 

[NomisST]

Heh, you sound like your in Calc 2. I just got to my sophmore year, 2nd year at Rutgers Engineering School. Doing EE, with a minor of East asian studies, taking a Samurai Class right now hehe. I feel bad for you cause I remember when I went through that, but in the end I understood it all and killed the final. Too bad I don't remember anything. Anyways I have to take up to Calc 5...so wish me luck...

 

[coomar]

you have a calc 5, i remember taking 3 calc's and then differential equations and complex functions which are extensions of a sort

 

[MrDudeMan]

Originally posted by: coomar
you have a calc 5, i remember taking 3 calc's and then differential equations and complex functions which are extensions of a sort

he isnt on semesters. if his college needs more than 3 semesters to fit in calculus the program just plain sucks. if it is on quarters, then thats another story.

 

[Loki726]

yeah, wtf is calc 5? We have regular calc, L'Hopital's rule/partial fractions/trig subs/power series/linear algebra, then vector calc, then diff eq's, then I sell my math books back for 30% of what I paid for them.

 

[MrDudeMan]

Originally posted by: Loki726
yeah, wtf is calc 5? We have regular calc, L'Hopital's rule/partial fractions/trig subs/power series/linear algebra, then vector calc, then diff eq's, then I sell my math books back for 30% of what I paid for them.

its 3 semester calc broken up into quarters basically...i hate schools that go on quarters

 

[IEC]

I'll be taking first year calc this fall... after taking AP Calc as a senior in HS

 

[Mday]

Originally posted by: ariafrost
I'll be taking first year calc this fall... after taking AP Calc as a senior in HS

I was a junior when I did calculus.

anyway.. ah, the days of HS... implicit differentiation generally means your "x" is on both sides. you do what you have to in order to "locate" all the X on one side.

Some schools include real analysis and complex analysis as calc 4 and 5 respectively.

 

[Gamingphreek]

I took Pre Calculus as a Junior, this year (Senior year.. HELL YEAH) im taking AP Calc.

Will my Ti-89 Titanium help me with AP Calc at all? This stuff looks kinda hard.

-Kevin

 

[MobiusPizza]

My Calculator tells me that
3A's answer is sin(1)
3B's anwer is 9

3A is pretty easy
secx = cos x, so the limit is lim (cosx*sin(cosx)), x-> 0
so 1 * sin 1
which is sin1

3C I don't know. Try expanding sin(3x) as -(sinx)^3
+ 3sinx(cosx)^2

 

[fatty4ksu]

Only way to own calc is to do millions of problems over and over.

 

[Loki726]

Originally posted by: Gamingphreek
I took Pre Calculus as a Junior, this year (Senior year.. HELL YEAH) im taking AP Calc.

Will my Ti-89 Titanium help me with AP Calc at all? This stuff looks kinda hard.

-Kevin

They have a calculator and non calculator section for the exam. I found my ti-89 useful for checking my answers and being able to use some numerical methods to make sure some of my approximations looked right. That being said, it will take you just as long to learn how to get the correct answers from your calculator as it will for you to learn the material itself.

The people who write the AP tests tend not to include the kind of 6th degree partial fractions expansion problems that I would rather just punch into my calculator than spend three sheets of paper solving. They would rather include some fairly basic examples of each topic that you can figure out in 5 seconds if you understand the topic, or can stare at for 15 minutes if you don't understand the topic.

If you don't understand the topic, don't expect your calculator to bail you out.

 

[dimalife]

Well i could probably help, but i'm angry with you.
You no longer stop for tea, coffee, or drugs.

I still have the same MSN, in case you wanna make up for lost time.



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