3 years ago

Find the 6th partial sum of the following geometric series. 1/2, -3/2, 9/2, -27/2

Mathematics

1 answer:

defon3 years ago

6 0

Answer:

243

Step-by-step explanation:

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3 years ago

Evaluate the line integral in Stokes? Theorem to evaluate the surface integral integrate S ( x F) n dS. Assume that n is in the

gtnhenbr [62]

Answer:

Step-by-step explanation:

Consider that F(x,y,z) = (x + y, y + z, z + z)

$r(t)=(cos t,4sint,\sqt{5}cost)\\r'(t)=(-sint,4cost,-\sqrt{5}sint)\\F(r(t))=[tex]\int\limits^{2\pi}_0 {F(r(t))r'(t)} \, dt \\\\=\int\limits^{2\pi}_0(cost+4sint,4sint+\sqrt{5}cost+cost)(-sint,4cost,-\sqt{5}sint)dt\\\\=\int\limits^{2\pi}_0(-sintcost-4sin^2t+16costsint+4\sqrt{5}cos^2t-5sintcost-\sqrt{5}sintcost)dt\\\\=\int\limits^{2\pi}_0(10sintcost-4sin^2t+4\sqrt{5}cos^2t-\sqrt{5}sintcost)dt\\\\=\int\limits^{2\pi}_0((10-\sqrt{5})sintcost-(4+4+\sqrt{5})sin^2t+4\sqrt{5})dt\\\\(10-\qrt{5})(0)-(4+4+\sqrt{5}(\pi)+4\sqrt{5}(2\pi)\\\\(\sqrt{5}-1)4\pi)$ [/tex]