How can i rationalize [h + sqrt(x+h) - sqrt(x)] / [ h ]
2007-09-12 15:26:38 · 5 answers · asked by Christine N 1 in Science & Mathematics ➔ Mathematics
well how do i simplify this problem??
2007-09-12 15:34:54 · update #1
It's already rationalized if there is no radical in the denominator.
If this is a calculus problem where you are finding a limit as h approaches 0, I suspect the top h shouldn't be there. Usually the problem goes:
[sqrt(x+h) - sqrt(x)]/h
Then you can simplify be multiplying both sides by the conjugate of the top, which is sqrt(x+h) + sqrt x.
After multiplying, you get
[(x+h) - x]/h(sqrt(x+h) = h/[h*sqrt(x+h)] = 1/(x+h), so that as h approaches 0, you get 1/x.
2007-09-12 15:30:05 · answer #1 · answered by jenh42002 7 · 1⤊ 1⤋
its already rationalized, i think. rationlize means to not make the denominator have a sqr root
2007-09-12 22:30:53 · answer #2 · answered by ►黄人◄ 6 · 0⤊ 1⤋
multiply numerator and denominator by [sqrt(x+h) + sqrt(x)] ...
[sqrt(x+h) - sqrt(x)]/h * [sqrt(x+h) + sqrt(x)]/[sqrt(x+h) + sqrt(x)] =
[(x+h) - x]/[h[sqrt(x+h) + sqrt(x)]] =
h/[h[sqrt(x+h) + sqrt(x)]] =
1/[sqrt(x+h) + sqrt(x)]
2007-09-12 22:34:57 · answer #3 · answered by ? 4 · 1⤊ 0⤋
[sqrt(x+h) - sqrt(x)] / [ h ] [sqrt(x+h) + sqrt(x)] / [ sqrt(x+h) + sqrt(x) ]
2007-09-12 22:32:55 · answer #4 · answered by Runa 7 · 0⤊ 0⤋
omg how should I know?!?!?!
2007-09-12 22:29:38 · answer #5 · answered by Anonymous · 0⤊ 3⤋