# What is the arc length of #f(x)=1/x-1/(x-4)# on #x in [5,oo]#?

If the upper limit is

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To find the arc length of the function ( f(x) = \frac{1}{x} - \frac{1}{x - 4} ) on the interval ( x \in [5, \infty) ), you can use the formula for arc length:

[ L = \int_a^b \sqrt{1 + (f'(x))^2} , dx ]

where ( f'(x) ) represents the derivative of ( f(x) ). First, find the derivative of ( f(x) ), then plug it into the formula and integrate over the given interval. Since the given interval is from 5 to infinity, the upper limit of integration will be infinity.

After integrating, you'll get the arc length of the function over the specified interval.

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