Worked example: differentiating polar functions | AP Calculus BC | Khan Academy

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An AP Calculus sample item where we find the rate of change of _ with respect to _.

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Комментарии
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i find it easier to differentiate with this simplification 3a Sin(a) Cos(a) there is the identity 2sin(a)cos(a)=sin(2a) deviding by two gives sin(a)cos(a) = sin(2a)/2 with the simplification 1.5a*sin(2a)

zhurs-mom
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THE CIRCLE FLIPS BECAUSE THE IS POSITIVE BETWEEN 0 AND 2π

Fanda
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Thank you so much! What a great video.

JamesBrodski
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You must carry an explanation, why you start from the inner loop and not outer even though r=0 for both the loops at theta=0.The reason is when theta= pi/2, the value of r=(3pi/2)sin(pi/2) and when theta =3pi/2, the value of r is not only negative, but also larger in magnitude=(9pi/2)sin (3pi/2) and is the part of outer(larger) loop.Hence you start from inner`through pi/2, and complete the cycle through outer`thro' 3pi/2.Hope this will clarify doubts in many minds.

XTSK
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Please, could someone help me; how can r be a function if it has multiple y outputs (the two loops) for the same x input value? I thought the definition of a function only allowed for there to be the same y outputs for different x values but not the other way around?

FA-tqip
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Can u do a no solution variable on both sides

Alexxxxx___
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Why the bigger loop is above the x axis and not below it. can someone explain, i didn't get sal's explanation.

aadilmiller