Mastering Limit Problems: Homework Statement & Solution | 65 Characters

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Homework Statement


lim
x>b (b-x)/sqr rootx-sqr root b





The Attempt at a Solution


I multilplied the top and bottom by b+x and found b-x^s on the top and x-b on the bottom
 
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Try multiplying through by the conjugate of \sqrt{x}-\sqrt{b}...
 
so would that be square root x plus square root b?
 
Yes it should be.
 
after factoring and simplifying i got my answer to be 2b
 
screamtrumpet said:
after factoring and simplifying i got my answer to be 2b

Not right. If you would show how you got there someone might be able to tell you why it's wrong.
 

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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