limh→ 0([([1/(√{5+h})]−[1/(√5)])/h])?

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limh→ 0([([1/(√{5+h})]−[1/(√5)])/h])?

is there a way to just look at these and know the answer?

I'm completely stumped.

2007-10-01 10:18:02 · 1 answers · asked by Ar J 2 in Science & Mathematics ➔ Mathematics

1 answers

lim h→ 0([([1/(√{5+h})]−[1/(√5)])/h]) = -1/(10√5) = -√5/50
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Reasons:
1/√(5+h) - 1/√5
= (√5 - √(5+h)/√[5(5+h)]
= -h/{(√5 + √(5+h)]√[5(5+h)]
= -h/(10√5), as h->0

2007-10-01 10:21:35 · answer #1 · answered by sahsjing 7 · 0⤊ 0⤋