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# 242hw11 - θ between 0 and 2 π for which the curve has...

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Math 242 Homework 11 Sections 012 and 014: Due MONDAY May 9th Section 050: Due Tuesday May 10th 1. Consider the parametric curve x = t + ln t , y = t - ln t , where 0 < t < . Find dy/dx and d 2 y/dx 2 . Find where the curve is increasing, decreasing, concave up, or concave down. Sketch the curve. 2. Given the polar equation r = 6 sin θ , 2a. Find all values of θ between 0 and 2 π for which the curve has horizontal tangents or vertical tangents. 2b. Draw a reasonable graph of the curve. Label at least three specific points. 2c. Find the area enclosed by the curve. 3. Given the polar equation r = sec θ tan θ , 3a. Find all values of
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Unformatted text preview: θ between 0 and 2 π for which the curve has horizontal tangents or vertical tangents. 3b. Draw a reasonable graph of the curve. Label at least three speciﬁc points. 3c. Find the area enclosed by the curve between θ = 0 and θ = π/ 4. 4. Given the polar equation r = 1-sin θ , 4a. Find all values of θ between 0 and 2 π for which the curve has horizontal tangents or vertical tangents. 4b. Draw a reasonable graph of the curve. Label at least three speciﬁc points. 4c. Find the area enclosed by the curve. 1...
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