# What is the arclength of #f(x)=(x-2)/x^2# on #x in [-2,-1]#?

This definite integral does not have an elementary intrinsic solution and would need to be solved numerically, using either a computer or estimated using the Trapezium Rule or Simpson's Rule

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To find the arc length of the function ( f(x) = \frac{x - 2}{x^2} ) on the interval ([-2, -1]), you can use the arc length formula:

[ L = \int_{-2}^{-1} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} , dx ]

where ( \frac{dy}{dx} ) represents the derivative of ( f(x) ) with respect to ( x ). Calculate ( \frac{dy}{dx} ), then substitute it into the arc length formula and integrate over the given interval to find the arc length ( L ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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