Recent content by hanelliot

hmm so solution must be wrong.. I wonder why no one pointed it out tho

lol yeah, been away from math for a long time so did forget it. don't worry about 16pi^3, it was done quickly and obv wrong.

Homework Statement a = 1/sqrt(29) * (-2*sint, 0, -2*cost) length of a is? Homework Equations The Attempt at a Solution ignoring 0, we have sqrt{[(-2*sint)/sqrt(29)]^2 + [(-2*cost)/sqrt(29)]^2}. I get 2/sqrt(29) but answer is [2*sqrt(2)]/sqrt(29). Can anyone do this step by step...

Homework Statement x = (-4\pisin\pit, 4\picos\pit, 1) what is the length of x?Homework Equations The Attempt at a Solution Well, I do realize that length of something is calculated by sqrt(x^2 + y^2) etc. However, when I plug in the numbers above, I get sqrt(16\pi^3 + 1), but the answer is...

L'hopital rule is fine of course.. you different top/bottom separately and get 1/3x^2, which is 1/12 if you plug in -2.

original question is actually cos(x) + cos(3x), not minus.. I made a mistake in post #5

using identities: cos(3x) = cos(2x+x) = cosx cos2x - sin^2x sinx cos(x) = cos(2x-x) = cosx cos2x + sin^2x sinx 2nd term cancels out and we get 2cosxcos2x at the bottom. I got some help from my TA and solved it, thanks for your help!

Thank you for your reply.. I worked out a new solution, can u see if anything's wrong? \int \frac{dx} {cosx-cos3x} = \frac{1}{4} (-(\frac{1}{2}) cot(\frac{x}{2}) - ln(cos(\frac{x}{2}) - sin(\frac{x}{2})) + ln(cos(\frac{x}{2}) + sin(\frac{x}{2}) - (\frac{1}{2}) tan(\frac{x}{2})) + C

it was a hint given by a TA.. I plugged in few numbers and the relationship seems to hold?

multivariable calculus II, I've been away from math for a long time and this is embarrassing.. anyways, ur answer = mine (plugged in few numbers to confirm), thanks all!

Homework Statement \int dx/(cosx + cos3x) Homework Equations The Attempt at a Solution Not sure if I'm doing this right. 1/cosx + cos3x = 1/2cosx * cos2x = cosx/cosx * 2cosxcos2x = cosx/2cos^2xcosx = (1/2)*(cosx)/[(1-sin^2x)(1-2sin^2x)] then we let t = sinx and get \int dx/(cosx...

Homework Statement derivative of x*sqrt[x/(2-x)] Homework Equations The Attempt at a Solution my friend got 1/(2-x) and I got {-(x-3)*[-x/(x-2)]^3/2}/x. Who's right?

you are right, my mistake I can show that with intuition and a sketch of plane/line but not sure how I should go about proving it formally.. maybe this Q is that simple and I'm overreacting

Homework Statement Let r be a line and pi be a plane with equations r: P + tv pi: Q + hu + kw (v, u, w are vectors) Assume v · (u x w) = 0. Show that either r ∩ pi = zero vector or r belongs to pi. Homework Equations n/a The Attempt at a Solution I get the basic idea behind it...

phi(20^100) = phi(4^100 * 5^100) = phi(2^200 * 5^100) = (2^200 - 2^199)(5^100 - 5^99) = 2^199(2-1) * 5^99(5-1) = 2^199 * 5^99 * 4 = 2^201 * 5^99. I don't understand line 4-7. Can anyone explain?