# How do you set up an integral from the length of the curve #y=1/x, 1<=x<=5#?

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To set up the integral for the length of the curve y = 1/x from x = 1 to x = 5, you use the formula for arc length:

L = ∫√(1 + (dy/dx)^2) dx

First, find dy/dx:

dy/dx = -1/x^2

Then, square it:

(dy/dx)^2 = 1/x^4

Next, add 1 to (dy/dx)^2:

1 + (dy/dx)^2 = 1 + 1/x^4

Now, take the square root:

√(1 + (dy/dx)^2) = √(1 + 1/x^4)

Now, integrate with respect to x from 1 to 5:

L = ∫(1 to 5) √(1 + 1/x^4) dx

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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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