Recent content by driscoll79

Hello there. Your setup wrt has one mistake; It should be: \pi\int{[(3-x^2)^2-(x^2+1)^2]dx} As for the second part, ideally you would not want to set this up wrt y, for the following two reasons: 1) It changes your method for finding volume from the washer method to cylindrical shells...

Jack - you were on the right track by figuring out the n+1 term. Use the ratio test. You should see fairly readily that the series converges to 0 as n goes to infinity.

Hey, The only thing I noticed is that your limits of integration seem to be off; t goes from -1 to 2, not -1 to 4. The integration is correct.

Hey Michael, I also got 8/48 using: x = \rho \sin\phi \cos\theta, y = \rho \sin\phi \sin\theta, z = \rho \cos\phi with 0 < \phi < \frac{\pi}{2}, 0 < \theta < \frac{\pi}{2}, 0 < \rho < \sqrt{2} so it looks to be correct, although I'd suggest checking everything one more time just to be sure.

What exactly are you stuck on? By inspection you know that if (A+Bi) divides your polynomial then (A-Bi) must also divide your polynomial because your polynomial does not have any complex coefficients. So, I'd recommend doing either a direct or indirect proof - though it seems as if a direct...

One big thing: The z-table in your book gives you P(z<Z) for a standardized normal random variable Z, not P(z>Z). So, P(z>1.8) = 1 - P(z<1.8) = 1 - phi(1.8). You may have already done that in your calculations but you did not specify that if you did. The formula I have for sigma is...

There seems to be some info missing here. Are X1, X2, and X3 independent? Are they discrete or continuous? Either way, what values can X1, X2, and X3 take? All this information is necessary in order to find the joint pdf of Y1, Y2, and Y3.

Hey Astro, You cannot do what you are suggesting for a pretty simple reason. Think of the one-dimensional number line. Each positive number x on the number line represents the distance between that number and 0. So, any line segment on the number line with length x lies on a closed interval...

Okay, I think I can help you with this one, but I'll leave the solving up to you. Think about it your p.d.f. of this function - it's binary, isn't it? In other words, if you define "success" to be getting HEADS on a given flip, then "failure" is not getting HEADS, right? So: P("success") = p =...

Taryn, for your last problem: \int x^6 \ln x dx Let u = \ln x and let dv = x^6 dx. It follows from there that: du = \frac{dx}{x} and that v = \frac{x^7}{7}. It's all integration by parts from there: \int u dv = uv - \int v du

I may be missing something here, but this doesn't look like a factorial to me. It looks like \prod_{k=1}^4 \frac{2k-1}{2k}. does it have to be in factorial form?

I'd recommend first finding the unit vector v = \frac{u}{||u||}, because you know that vector has a magnitude of 1. Then, you know that ||kv||=\sqrt{17}, and you know that ||v||=1, so k=\sqrt{17}. So, your new vector...

Yes, curves can be orthogonal to one another, and you've already determined that these two curves are in fact orthogonal to one another because their respective derivatives are lines with negative reciprocal slopes. You can determine the points of intersection of the curves by setting them equal...

Yes, that's correct. \frac{(4x-3)^3}{12} is one primitive function, where C=0. Likewise for your polynomial. \frac{(4x-3)^3}{12}+C defines the entire family of primitive functions, where C can take any value.

Yes, it is. Similarly, \lim_{x\rightarrow 0} \frac{sin(x)}{x} = 1. The intuitive (read: non-Calc) way to see this is to set up a table with columns x and sin(x), and use your calculator to see what happens to sin(x) as your x value gets closer to (but not equal to) 0. You should see that as x...