Recent content by tsamocki

Edit: F(a) = \int_{\text{0}}^1 3y^2 \, dy, Sorry, i previously responded via phone.

You mean this: F(a) = \int_{\text{0}}^1 y^3 \, dx,

Homework Statement Example 5.1.4: Y is a continuous random variable on the interval (0; 1) with density function fY (y) = {3y2 0 < y < 1 {0 elsewhere what is the cumulative distribution function of Y ? Homework Equations The relationship between a continuous random variable and...

Sorry for the delayed response, been studying for other finals. Here is where i am stuck. For the x partial derivative: \partial / \partialx= -rsinθ+cosθ For the y partial derivative: \partial / \partialy= sinθ+rcosθ I know this is incorrect because i was informed by my professor that...

Homework Statement The Laplace operator Δ is defined by: Δ= Show in polar coordinates r and Θ, that the Laplace operator takes the following form: http://upload.wikimedia.org/wikipedia/en/math/0/7/a/07a878276cffd0c680f3f827204aba24.png Homework Equations x=rcos(Θ), y=rsin(Θ), r ≥ 0, Θ ∈...

Would i need to integrate it in order to get a function of 0, r(0) = (e,0)? ∫rdr = e^(cos(t))+constant, ∫rdr = sin(t)+constant; if t=0, the function turns into the desired form. Is this on the right track?

Yes i am! It is given in wolfram mathematica form T(t) = (-exp(cos(t))sin(t), cos(t)); so now that you think about it, i could see it being T(t) = -sin(t)e^(cos(t)), cos(t). I apologize for my errors.:blushing:

Sorry, maybe I've omitted something important: for each (t), the function T provides a tangent vector to an assortment of curves. The curve r exists in this assortment; find r that satisfies r(0) = (e^1, 0).

Homework Statement Find a tangent vector r that satisfies r(0)= (e^(1),0) given T(t) = (-e^(cos(t)sin(t)),cos(t)), where t is an element of [0,2π] Homework Equations Tangent vector T = r'(t)/(norm(r'(t)) The Attempt at a Solution I was thinking that r(t) = ∫r'(t), and that the norm of r(t)...

r^2 = x^2 + y^2 + z^2 r^2 = (cos(t^3)sin(t))^2 + (sin(t^3)sin(t))^2 + (cos(t))^2 r^2 = [cos^2(t^3) sin^2(t)] + [sin^2(t^3)sin^2(t)] + [cos^2(t)] since r^2 = 1, and the other side simplifies to 1, the graph of the function lies on the surface of a sphere? Since it simplifies to 1...

Homework Statement r(t) = [cos(t^3)sin(t), sin(t)sin(t^3), cos(t)], where t is an element of (0,2pi). Show that the graph of this function is on the surface of a sphere. Then find it's radius. Homework Equations T(t) = r'(t)/norm[r'(t)] equation for a sphere in 3-space: r^2=x^2+y^2+z^2...

Simplifying the general term, i was left with: -(lim (-1)^(n+1)/(n(n+1))), which when n-> infinity, the limit is zero. Normally when you have a function that has an exponential sum (^(n+1)), wouldn't you make the entire limit be an exponent of e? I did forget the squeezing theorem :-*

Almost; after simplifying , i am still left with a numerator of (-1)^(n+1), which confuses me. Is it safe to assume that as n -> infinity, the +1 is trivial, and can instead take the numerator to be simply (-1)^n and the denominator to be n^2-n (which is easy to solve)? P.S. The original...

Yes, i did mistakenly leave out that parentheses. It should look like this: (-1)^(n+1)*((1/n)-(1/(n+1))) which is not the same answer as what Dick provided because i am subtracting the (1/(n+1)) from (1/n). Unless of course i am mistaking something (which is very possible lol). Am...

Yes, that works. Is it possible to have more than one solution? For example, your solution gave me an idea: (-1)^(n+1)*((1/n)-(1/n+1)) seems to work as well.