How do you graph #r^2=  cos theta#?
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To graph (r^2 = \cos(\theta)), we first need to recognize that (r) is the distance from the origin to a point on the graph, and (\theta) is the angle measured counterclockwise from the positive xaxis to the point.

Consider the Range of (\cos(\theta)): The range of the cosine function is ([1, 1]). Since we have (\cos(\theta)), the range will be ([1, 0]).

Square Root: Notice that (r^2) will always be nonnegative, so (\cos(\theta)) must also be nonnegative. This occurs when (\cos(\theta) = 0), which happens at (\theta = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, \ldots).

Plotting the Graph: At these values of (\theta), (r^2 = \cos(\theta) = 0), so (r = 0). This means the graph consists of points where (r = 0), which is just the origin.

Summary: The graph of (r^2 = \cos(\theta)) is a single point at the origin (0, 0).
So, the graph is just a single point at the origin (0, 0).
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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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