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Mathematical Writing with Evidence
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Grade Level
Calculus II
CAL2.156 Mathematical Writing with Evidence
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For the polar curve r = 2 cos theta, a solution claims the tangent is horizontal at theta = pi/4. Which sentence best supports the claim?
A
The tangent is horizontal because r is positive at theta = pi/4.
B
At theta = pi/4, x = r cos theta = 2cos
2
theta and y = r sin theta = sin 2theta, so dx/dtheta = -2 and dy/dtheta = 0, giving dy/dx = 0.
C
The tangent is vertical because dr/dtheta = -2sin theta is negative at theta = pi/4.
D
The tangent cannot be determined because polar curves do not have rectangular slopes.
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