Proof of Limit Algebra: k + a_[n] → k + lim(a

mitch_nufc · 2009-05-07T12:13:33+00:00

Let a_[n] be a sequence tending to a and let k be a real number. Give an epsilon - N proof that lim (k + a_[n]) = k + lim(a_[n]) the the limits are both as n-> infinity I'd really appreciate some help here people. Thanks

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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Proof of Limit Algebra: k + a_[n] → k + lim(a_[n])

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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