# How do you find the arc length of a polar curve?

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To find the arc length of a polar curve, you can use the formula:

[ L = \int_{\alpha}^{\beta} \sqrt{r(\theta)^2 + \left(\frac{dr}{d\theta}\right)^2} , d\theta ]

Where:

- ( L ) is the arc length,
- ( r(\theta) ) is the polar function,
- ( \frac{dr}{d\theta} ) is the derivative of the polar function with respect to ( \theta ),
- ( \alpha ) and ( \beta ) are the limits of integration.

You integrate this expression with respect to ( \theta ) over the given range of ( \theta ) values to find the total 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.

- What is the Cartesian form of #(-49,(-3pi)/4)#?
- What is the area inside the polar curve #r=1#, but outside the polar curve #r=2costheta#?
- What is the Cartesian form of #(12,(14pi)/3))#?
- What is the equation of the tangent line of #r=cos(2theta-pi/4)/sintheta - sin(theta-pi/8)# at #theta=(-3pi)/8#?
- What is the slope of the tangent line of #r=3sin(theta/2-pi/4)# at #theta=(3pi)/8#?

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