# How do you find the arc length of the curve #y=(x^2/4)-1/2ln(x)# from [1, e]?

And you have to simplify down to a perfect square and then take the square root. The simplification is the hard part. Afterwards it's very simple (keep reading).

You can find the derivation for the arc length at the bottom if you don't remember it or don't have it derived.

Since we are in a positive domain, all this works out to be:

Derivation The arc length can be derived, if you forget the (rather simple) formula. Since it really is just an accumulation of really short straight lines, you can use the distance formula and modify it in such a way that it works for a specific variable using the definition of the derivative.

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To find the arc length of the curve y = (x^2/4) - (1/2)ln(x) from x = 1 to x = e, you use the arc length formula for a curve given by y = f(x) from x = a to x = b:

Arc Length = ∫[a, b] √(1 + (f'(x))^2) dx

First, find f'(x) which is the derivative of y with respect to x. Then, substitute f'(x) into the arc length formula and integrate from x = 1 to x = e to find the arc length of the curve.

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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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