Help understanding what limits are

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Homework Statement


http://www4c.wolframalpha.com/Calculate/MSP/MSP18091a03ad70feibdhb300005da572897hebg236?MSPStoreType=image/gif&s=52&w=143&h=42


Homework Equations


lim x->2+ (x^2 - 3x + 2) / (x^3 - 4x)


The Attempt at a Solution


I plugged in 2 for x and it was 0/0 so then I divided each term by the highest power, which is x^3 but I still got 0/0. The answer is 1/8 but I don't know how to get it.
 
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azncocoluver said:

Homework Statement


http://www4c.wolframalpha.com/Calculate/MSP/MSP18091a03ad70feibdhb300005da572897hebg236?MSPStoreType=image/gif&s=52&w=143&h=42


Homework Equations


lim x->2+ (x^2 - 3x + 2) / (x^3 - 4x)


The Attempt at a Solution


I plugged in 2 for x and it was 0/0 so then I divided each term by the highest power, which is x^3 but I still got 0/0. The answer is 1/8 but I don't know how to get it.

Factor the numerator and denominator!
 
Last edited by a moderator:


Oh yeah! I totally forgot about that. Thank you!
 

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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