Question Error? (epsilon-delta proof of a limit)

Mustard
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Homework Statement
look at snippet
Relevant Equations
look at snippet
I can not follow this mathematically. I am guessing one of the signs is incorrect?
Can anyone verify ?
 

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What is ##|(\frac{3}{4}x + 1) - 7|##?
 
etotheipi said:
What is ##|(\frac{3}{4}x + 1) - 7|##?
@Mustard, after you simplify the above, factor out 3/4 from both terms inside the absolute value signs.
 
There is one error in the question: the steps are in reverse order.
 
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The implication signs are missing: ##\Leftarrow## or ##\Leftrightarrow## would do.
 

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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