# How do you find the area of the region bounded by the polar curves #r=1+cos(theta)# and #r=1-cos(theta)# ?

The region bounded by the polar curves looks like:

Since the region consists of two identical leaves that are symmetric about the

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To find the area of the region bounded by the polar curves ( r = 1 + \cos(\theta) ) and ( r = 1 - \cos(\theta) ), integrate the difference of the two curves from their points of intersection. The points of intersection are found by setting the two equations equal to each other and solving for ( \theta ). Then, integrate the difference between the larger curve and the smaller curve with respect to ( \theta ) over the interval of intersection. This gives the area enclosed by the curves.

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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 slope of the tangent line of #r=thetacos(theta/4-(5pi)/3)# at #theta=(pi)/3#?
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- The tangent to #y=x^2e^x# at #x=1# cuts the #x# and #y#-axes at #A# and #B# respectively. Find the coordinates of #A# and #B#.?
- What is the Cartesian form of #(2,(pi)/4)#?
- What is the polar form of #( 17,15 )#?

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