What are the Steps for Finding Vertical Asymptotes in Polynomial Functions?

rteng
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Alright, I know how to find the horizontal asymptotes

but the vertical asymptotes?

I tried dividing the polynomials but maybe I am not doing it correctly because I cannot get a normal answer...

and I am unsure how to factor the denominator.
 
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2x^3-4x^2-2x+4=2x^2(2x-4)-1(2x-4)

does that help you?
 
yes that makes more sense thanks

didn't consider that
 
and then just check to see what makes the function undefined
 

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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