<PRE><B>Question 344844</B>
[f(x+h)-f(x)]/h 
g(x)=3sqrt of x
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f(x+h) = 3sqrt(x+h)
f(x)   = 3sqrt(x)
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[f(x+h)-f(x)]/h = [3[sqrt(x+h)-sqrt(x)]]/h
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Multiply numerator and denominator by sqrt(x+h)+sqrt(x) to get.
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= (3/h)[(x+h)-x]/[sqrt(x+h)+sqrt(x)
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= (3/h)[h]/[sqrt(x+h)+sqrt(x)
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= 3/[sqrt(x+h)+sqrt(x)]
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Notice, if you let h approach zero, the quotient approaches 3/(2x^(1/2))
= (3/2)x^(-1/2)
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Cheers,
Stan H.</PRE>