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The Math Help Thread
- Thread starter -COOLIO-
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As posted before, use the chain rule. You know, derivative of the "outside" times the derivative of the "inside."Guled said:
So the derivative of lnx is 1/x and the derivatives of secx and tanx are secxtanx and (secx)^2, respectively.
Same thing for the y'' of the second one. It's incredibly easy to find the derivative of e functions, just repeat what you did when you got y' plus the fact that you have to use the power rule.
I'd post a more detailed answer but it's really hard and annoying to post complicated math functions.
Scalemail Ted
Member
Can anyone help solve this?
I'm trying to solve for the arc length.
I'm trying to solve for the arc length.
Scalemail Ted
Member
Thanks for the hints.
I got 4pi
Is that correct?
I got 4pi
Is that correct?
I'm working on an assignment due tomorrow and I lent out my notes thinking I wouldn't be needing them. It turns out I might, and then book doesn't really explain this stuff all that well, so here's hoping GAF knows what to do.
I have no idea if this is right or why it's right if it is. Any help?
Right now I'm thinking I need to take a double integral of the equation with the integrals evaluated from 0 to 4 and -1 to 1:
I have no idea if this is right or why it's right if it is. Any help?
Scalemail Ted
Member
Quick math question.
However:
how do i have the denominator as 2x --> but the book has x??????
What did i do wrong???
However:
how do i have the denominator as 2x --> but the book has x??????
What did i do wrong???
TimesEunuch
Member
They're the same thing, the only difference is the integration constant. You can pull the factor of 2 out as -3 ln 2, and absorb it into the C.Scalemail Ted said:However:
how do i have the denominator as 2x --> but the book has x??????
What did i do wrong???
Guled said:Can anyone help me with this one question?
the answer is 0, but I don't understand how to do it.
Well, even though I lack the vocabulary for talking about maths in English:
As x approaches 0-, 1/x will approach negative infinity. e^(negative infinity) is incredibly small. The x below won't grow fast enough to be able to stop the whole function from approaching zero.
hemtae
Member
Guled said:Can anyone help me with this one question?
the answer is 0, but I don't understand how to do it.
looks like something that will involve L'Hopital's rule
http://en.wikipedia.org/wiki/L'Hospital's_rule
hemtae said:
Unfortunately, that probably won't help since he'll have to multiply the function by d/dx(1/x) due to e(^1/x), getting the lower part to grow smaller even faster.
Integrating both the e^(1/x) and x won't help either; he'll just end up with virtually the same function.
Jonsoncao
Banned
a little substitution would be helpful, let y = 1/xGuled said:Can anyone help me with this one question?
the answer is 0, but I don't understand how to do it.
then when x approaches 0^-, y approaches -inf
the limit becomes: (I ll use a little TeX here, _ means subscript, ^ means supscript)
lim_{x \rightarrow 0^-} e^{1/x}/x = lim_{y \rightarrow -\infty} e^y/(1/y) = lim_{y \rightarrow -\infty} y/e^{-y}
use LHopital rule for the last expression(infinity over infinity type) u ll get the answer
another explanation would be e^{1/x} convergence rate is x to the infinite power, it is a lot faster than x to the first power, when x is near 0 minus
I used to teach my CS students Cal III, so I am very positive with my answer above
alexthekid
Member
-COOLIO- said:
This might be the greatest site i have ever seen, thanks thanks thanks. I am studying fourier series and fourier transform right now, but cant find them there do anybody now if they have another name in english?(I understand that it is a stupid question if they are never told fourier in english, but i thought that they may have two names for it.)
Jonsoncao
Banned
alexthekid said:
No, Fourier transform is just Fourier transform
it has something to do with the Laplace transform, maybe you could google frequency domain for more info
basically an FT transforms your time domain stuffs(function of t, functionals on time dependent function space) into frequency domain stuffs
Uncompromisable
Banned
I need some simple cal help:
f(x) = (2x+5)^5 ; f'(x) = 10(2x+5)^4
right?
f(x) = (x^2+5)^6 ; f'(x) = 12x(x^2+5)^5
so far so good
now this:
f(x) = (x^3+5)^6 ; f'(x) = 18x^2(x^3+5)^5
No?
Doesn't seem to work: http://integrals.wolfram.com/index.jsp?expr=18x^2(x^3%2B5)^5&random=false
What's the rule with this stuff? I thought I had it but I dont...
is the rule this?
f(u) = (u + c)^k; f'(u) = ku'(u+c)^(k-1) ?
f(x) = (2x+5)^5 ; f'(x) = 10(2x+5)^4
right?
f(x) = (x^2+5)^6 ; f'(x) = 12x(x^2+5)^5
so far so good
now this:
f(x) = (x^3+5)^6 ; f'(x) = 18x^2(x^3+5)^5
No?
Doesn't seem to work: http://integrals.wolfram.com/index.jsp?expr=18x^2(x^3%2B5)^5&random=false
What's the rule with this stuff? I thought I had it but I dont...
is the rule this?
f(u) = (u + c)^k; f'(u) = ku'(u+c)^(k-1) ?
Roude Leiw
Member
Uncompromisable said:
yours is correct, wolfram does the integral, you are doing the derivative.
PolarBearsClub
Member
I have a final a few hours so any help is appreciated.
A deposit of $1000 is made to a bond fund. The amount triples in 10 years. Find the annual interest rate if interest is compounded monthly.
I'm pretty sure I have it set up right:
3000=1000(1+r/12)^120
But I'm not sure where to take it from there. The answer is supposed to be
12(e^(ln3/120)-1)
A deposit of $1000 is made to a bond fund. The amount triples in 10 years. Find the annual interest rate if interest is compounded monthly.
I'm pretty sure I have it set up right:
3000=1000(1+r/12)^120
But I'm not sure where to take it from there. The answer is supposed to be
12(e^(ln3/120)-1)
PolarBearsClub said:
Divide both sides by 1000 to get:
3=(1+r/12)^120
Take the logarithm of both sides:
ln(3)=ln((1+r/12)^120)
With the logarithm, you can take out the exponent:
ln(3)=120*ln(1+r/12)
Divide:
ln(3)/120=ln(1+r/12)
Make each side powers of e:
e^(ln(3)/120)=e^(ln(1+r/12))
Now you can also undo the logarithm on the right hand side since e^ln(x)=x:
e^(ln(3)/120)=1+r/12
Solve for r.
I wouldn't know how to prove it, but I think it makes sense for x values greather than or equal to one from just looking at the unit circle and the graph of sin(x). The range of sin(x) is only from -1 to 1, so the only way where x>sin(x) could possibly be false is when x<1. I don't know how you would prove it for those values though. I'm stumped.
whatsinaname
Member
-COOLIO- said:
Been some time, I don't know if this is valid.
Consider f(x) = x - sin(x)
f'(x) = slope = 1 - cos(x) > 0
f(0) = 0
So f(x) > 0
x - sin(x) > 0
x > sin(x)
Scalemail Ted
Member
Find an equation of the tangent to the curve at the point coresponding to the given value of the parameter.
t = 1
First we must find the (x,y) coordinate in which t = 1.
,
Which yields the point (e,1). Next we must find the slope of the line at the given point by finding the value of dy/dx at t=1.
Therefore:
When t = 1 dy/dx = -2/e
So the equation of the line is
I understand everything here up until the end. Where did the +3 come from????
TimesEunuch
Member
You know the tangent line has the equation y = -2/e x + const. To find the constant, just note that the line has to pass through the point (x,y)=(e,1) (i.e. the point on the original curve where t=1).Scalemail Ted said:
close to the edge
Member
Do you mean the functions? (y = sin(x) and y = x respectively) If yes, one idea might be that sin(x) has a limit at x = 1 and y = x doesn't.-COOLIO- said:
-COOLIO-
The Everyman
agh i forgot to check back here, this would of worked. thanks bro. i have to make sure to remember this.whatsinaname said:Been some time, I don't know if this is valid.
Consider f(x) = x - sin(x)
f'(x) = slope = 1 - cos(x) > 0
f(0) = 0
So f(x) > 0
x - sin(x) > 0
x > sin(x)
that's true but that doesnt mean sinx couldnt have been bigger than x at reaaally small values (which it isnt)close to the edge said:
liquidspeed
Member
isnt the integrating factor supposed to be I(x) = e^(integral: (P(x)dx )torontoml said:
im only 3 lecures into diffEq, we hit second order equations either this week or next
Particle Physicist
between a quark and a baryon
.
innervision961
Member
please forgive this easy question, but can GAF tell me the answer?
4y+7=2y-5
4y+7=2y-5
innervision961
Member
Diebuster said:
Thanks! I see what I did wrong now
Roude Leiw
Member
what kind of shape do these equations have:
x+y+z = 1
1/4 * (x+1)² + y² + z² = 1
thanks!
x+y+z = 1
1/4 * (x+1)² + y² + z² = 1
thanks!
That first one is a plane in 3-D space.
That second one appears to be an ellipsoid... x^2 + y^2 + z^2 = 1 would be a sphere, so I assume it is shifted to the left by 1 unit on the x-axis, and also stretched on the x-axis by a factor of 4. Not 100% sure, though.
Edit: Stretched by a factor of 2, not 4. My bad.
That second one appears to be an ellipsoid... x^2 + y^2 + z^2 = 1 would be a sphere, so I assume it is shifted to the left by 1 unit on the x-axis, and also stretched on the x-axis by a factor of 4. Not 100% sure, though.
Edit: Stretched by a factor of 2, not 4. My bad.
I have a question regarding differentiation :
when differentiating a little more difficult functions is there a step by step approach one should take or is it always situational?
allow me to elaborate
lets just imagine some arbitrary function , f(x) = ( 2x^2 * cos(3x)^5) / ( sqrt (1/x)*sin*2x )
what should one start with? Can you start by differentiating the numerator and denominator respectively with the help of the chain rule and then proceed to use the quotient rule?
when differentiating a little more difficult functions is there a step by step approach one should take or is it always situational?
allow me to elaborate
lets just imagine some arbitrary function , f(x) = ( 2x^2 * cos(3x)^5) / ( sqrt (1/x)*sin*2x )
what should one start with? Can you start by differentiating the numerator and denominator respectively with the help of the chain rule and then proceed to use the quotient rule?
Roude Leiw
Member
Feep said:
thank you.
i couldnt find any information on ellipsoids shifted on their x axis though, thats why i am not sure.
http://en.wikipedia.org/wiki/Ellipsoid
AlternativeUlster
Absolutely pathetic part deux
Tater Tot said:
You can turn them into fractions. 2.5 is 5/2. So 3 + 5z/2 + 5 = 9z/2 - 6 then it is 8 + 5z/2 = 9z/2 - 6 then 14 = 4z/2 then 14 = 2z then z = 7.
Also COOLIO IS A FOOLIO.
It's fairly step-by-step. You always do the "outermost" operation first. In this case, the '/' is first, so quotient rule is numero uno...though I hate the quotient rule, I'll usually flip the exponent and use product rule instead. Then, when you need du or dv, you use the appropriate rule on that part of the function, and so on and so forth.Corky said:
If you're familiar with computer science, it's a recursive process.
quilter46761
Member
Corky said:
You can also use logarithms too - take the log of both sides and simplify by log properties. It then turns into addition and subtraction, and you can implicitly differentiate from there.
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