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All of them ahahah

LOL I have done way too much integration. Should've specified they're all positive.

$ If $ \sum_{k=1}^{\infty}{a_k}dx $ converges does $ \sum_{k=1}^{\infty}{(-1)^n a_k}dx $ converge? $

All these identities that I don't know :'( rip

Where did you get lambda ^3 from ? Is it because its a 3 by 3 matrix?

I was looking for this everywhere.

1) How can you determine the nullity of this transformation without finding the matrix? Also does P_2 -> P_3 mean that we put in a polynomial of degree 2 and we get out one of degree 3 ? T(p(x)) = (x^2 + 1)p'(x) -2xp(x) P_2 -> P_3 2) Let A be a fixed 3 x 3 matrix and define a linear map T...

Makes sense now :P so my integral becomes : \sqrt{2} (\int_0^{\pi}{\frac{\sin{x}}{\sqrt{1-\cos{x}}}} - \int_{\pi}^{2\pi}... thanks !!

I still don't get the answer and whats wrong with my way of integration?

Re: MATH1231/1241/1251 SOS Thread Wolfram the hell out of integration

r^2 = 1 + 2\cos{\theta} + \cos^2{\theta}, \frac{dr}{d\theta} = -\sin{\theta} I = \int_0^{2 \pi}{\sqrt{2 + 2\cos{x}}}dx I = \sqrt{2} \int_0^{2 \pi}{\sqrt{1 + \cos{x}}}dx I = \sqrt{2} \int_0^{2 \pi}{\frac{\sin{x}}{\sqrt{1 - \cos{x}}}}dx I = 2\sqrt{2} [-\sqrt{1- \cos{x}}]_0^{2 \pi} ...

ahahahaha

When you evaluate the integral you get 0 ?

Re: MATH1231/1241/1251 SOS Thread This was the question I asked about, trying to figure out the matrix first then multiplying. :)

$ Find the length of the cardioid $ r = 1 + \cos{\theta}

This makes sense but when we do it by force we get |xlnx| < e and this isnt true for all x? ( what i did was ratio test is less than 1) Edit: nvm got it was missing a k+1 in the denominator

Find the radius of convergence of \sum{\frac{(\ln{(x)}x)^k}{k^k}}

So it didnt even matter what was in the numerator with ln's ? Youd still replace it wth something such that the bottom degree - top degree = something greater than 1? Isnt this fudging it?