How do you find the arc length of the curve #y=sqrt(cosx)# over the interval [pi/2, pi/2]?
as:
integrating over the interval we have:
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To find the arc length of the curve (y = \sqrt{\cos(x)}) over the interval ([ \frac{\pi}{2}, \frac{\pi}{2}]), you use the arc length formula:
[ L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} , dx ]

Find the derivative of (y = \sqrt{\cos(x)}): [ \frac{dy}{dx} = \frac{1}{2} \sqrt{\frac{1}{\cos(x)}} \cdot (\sin(x)) = \frac{\sin(x)}{2\sqrt{\cos(x)}} ]

Square the derivative and add 1: [ 1 + \left(\frac{dy}{dx}\right)^2 = 1 + \left(\frac{\sin(x)}{2\sqrt{\cos(x)}}\right)^2 ]

Integrate ( \sqrt{1 + \left(\frac{dy}{dx}\right)^2} ) from (\frac{\pi}{2}) to (\frac{\pi}{2}): [ L = \int_{\frac{\pi}{2}}^{\frac{\pi}{2}} \sqrt{1 + \left(\frac{\sin(x)}{2\sqrt{\cos(x)}}\right)^2} , dx ]

Solve the integral to find the arc length.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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