SOLUTION: lim {√(x-q)-√(p-q)}/x^2-p^2 (p>q)is evaluated as
x-->p
A)1/p√(p-q)
B)1/4p√(p-q)
C)1/2p√(p-q)
D)none of these
Algebra.Com
Question 1044609: lim {√(x-q)-√(p-q)}/x^2-p^2 (p>q)is evaluated as
x-->p
A)1/p√(p-q)
B)1/4p√(p-q)
C)1/2p√(p-q)
D)none of these
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Rationalize the numerator:
\left(\frac{\sqrt{x\,-\,q}\ +\ \sqrt{p\,-\,q}}{\sqrt{x\,-\,q}\ +\ \sqrt{p\,-\,q}}\right)\right\])
}{\left(x^2\ -\ p^2\right)\left(\sqrt{x\,-\,q}\ +\ \sqrt{p\,-\,q}\right)\right\])
\left(x\ +\ p\right)\left(\sqrt{x\,-\,q}\ +\ \sqrt{p\,-\,q}\right)\right\])
\left(\sqrt{x\,-\,q}\ +\ \sqrt{p\,-\,q}\right)\right\])
Evaluate at 
\left(\sqrt{x\,-\,q}\ +\ \sqrt{p\,-\,q}\right)\right\]\ =\ \frac{1}{2p\left(2\sqrt{p\,-\,q}\right)}\ =\ \frac{1}{4p\left(\sqrt{p\,-\,q}\right))
John
My calculator said it, I believe it, that settles it
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