As posted before, use the chain rule. You know, derivative of the "outside" times the derivative of the "inside."Guled said:alright, got the last one. Still stumped on the first and y'' for the second.
Romaji said:You have x and y defined in terms of t. Take the derative of each with respect to t (i.e., find dx/dt and dy/dt). Plug them into the appropriate spots, simplify*, and integrate.
* Hint:cos(a)^2 + sin(a)^2 = 1
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:Find the volume of the solid enclosed by the paraboloid z = 2 + x^2 + (y - 3)^2, the xy plane, and the vertical planes x = -1, x = 1, y = 0, y = 4.
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.
Guled said:Can anyone help me with this one question?
the answer is 0, but I don't understand how to do it.
hemtae said:looks like something that will involve L'Hopital's rule
http://en.wikipedia.org/wiki/L'Hospital's_rule
thats what I thought, but I get -(e^(1/x))/x^2 which doesn't make it betterhemtae said:looks like something that will involve L'Hopital's rule
http://en.wikipedia.org/wiki/L'Hospital's_rule
Guled said:thats what I thought, but I get -(e^(1/x))/x^2 which doesn't make it better
edit: beaten by Leezard
hemtae said:Well I went off in the wrong direction
Anyways (e^(1/x))/x = (e^(-x))/x
= 1/(e^x)/x= x/(e^x)= 0/1= 0
hope you can follow that
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.
-COOLIO- said:
alexthekid 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.)
Uncompromisable said: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) ?
PolarBearsClub said: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)
What kind of proof do you need? A real fucking hardcore QED proof, or a graph?-COOLIO- said:i might be brain farting, but is there an easy proof as to why x > sin(x) for all x greater than 0?
-COOLIO- said:i might be brain farting, but is there an easy proof as to why x > sin(x) for all x greater than 0?
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
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:I understand everything here up until the end. Where did the +3 come from????
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:i might be brain farting, but is there an easy proof as to why x > sin(x) for all x greater than 0?
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: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.
isnt the integrating factor supposed to be I(x) = e^(integral: (P(x)dx )torontoml said:Having some trouble with this one:
The differential equation (3xy^2 - 2y)dx + (5x^2y^2 - 3x)dy = 0
I need to find the integrating factor in the form u=x^my^n.
innervision961 said:please forgive this easy question, but can GAF tell me the answer?
4y+7=2y-5
Diebuster said:4y + 7 = 2y - 5
2y + 7 = -5
2y = -12
y = -6
ya, but I'm having trouble getting P(x) or f(x) whatever you want to use. I thought f(x) needed to be just a function of only x and I can't get that.liquidspeed said:isnt the integrating factor supposed to be I(x) = e^(integral: (P(x)dx )
im only 3 lecures into diffEq, we hit second order equations either this week or next
Feep said: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.
Tater Tot said:How do I get rid of the decimals?
3+2.5(z+2)=4.5z-6
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: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?
You could also multiply everything by 2, so it looks like:Tater Tot said:How do I get rid of the decimals?
3+2.5(z+2)=4.5z-6
Corky said: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?