What is the arclength of the polar curve #f(theta) = cos^2theta-3sin^2theta # over #theta in [pi/3,pi/2] #?
Arclength is given by:
Expand the square and combine terms:
Complete the square in the square root:
Factor out the larger piece:
Apply binominal expansion:
Simplify:
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The arc length of the polar curve ( f(\theta) = \cos^2(\theta) - 3\sin^2(\theta) ) over the interval ( \theta ) in ( \left[\frac{\pi}{3}, \frac{\pi}{2}\right] ) is ( \frac{\sqrt{10}}{3} ).
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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.
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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