`f(x) = 4/sqrt(4)` Find the derivative of the function by the limit process.

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Chapter 2, 2.1 - Problem 24 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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By limit process, the derivative of a function f(x) is :-

`f'(x) = lim_(h -> 0) [{f(x+h) - f(x)}/h]`

Now, the given function is :-

`f(x) = 4/sqrt(4)`

Thus, `f'(x) =lim_(h -> 0) [{f(x+h) - f(x)}/h]`

or, `f'(x) = lim_(h -> 0) [ {(4/sqrt(4)) - (4/sqrt(4))}/h] = [0/h] = 0`

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hkj1385 | (Level 1) Assistant Educator

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As per the limit process:-

f'(x) = lim h ---> 0  [f(x+h) - f(x)]/h

Now, f(x) = 4/sqrt(4)

Thus, f(x+h) = 4/sqrt(4)

Hence , f'(x) = lim h-->0 [ {4/sqrt(4)} - {4/sqrt(4)}]/h = 0/h

or, f'(x) = 0

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