Limit definition of the derivative
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Limit definition of the derivative

[From: ] [author: ] [Date: 11-10-10] [Hit: ]
An explanation would be greatly appreciated.-f (x) = (f(x+h) - f(x))/h as the limit of h goes to 0.From here you need to use the algebraic conjugate, √(2(x+h)-1) + √(2x-1) and multiply top and bottom by that. Get rid of the h by cancelling then sub in 0 for h when there isnt an h that causes problems, like if it makes the denominator 0.......
Can anyone help me with this problem? I've been trying to figure it out but no dice.
Use the limit definition of the derivative to find f '(x) for f(x)= √(2x-1). An explanation would be greatly appreciated.

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f '(x) = (f(x+h) - f(x))/h as the limit of h goes to 0.

This problem would start as [√(2(x+h)-1) - √(2x-1)]/h

From here you need to use the algebraic conjugate, √(2(x+h)-1) + √(2x-1) and multiply top and bottom by that. Get rid of the h by cancelling then sub in 0 for h when there isn't an h that causes problems, like if it makes the denominator 0.
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