Solve Limit Calc Problem: 3^(2x) - 1 / 3^(2x) + 1 • Physics Forums

FrostScYthe · 2005-12-08T06:10:30+00:00

Hi, I did this limit, I know what it is by intuition, I just don't know how to mathematically calculate it. lim 3^(2x) - 1 x->-inf ---------- = -1 3^(2x) + 1

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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Solve Limit Calc Problem: 3^(2x) - 1 / 3^(2x) + 1

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

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