Find the slopes of the curves in Exercises 17–20 at the given points. Sketch the curves along with their tangents at these points. 17. Cardioid r=-1 + cos 0; 0 = ±#/2 18. Cardioid r=-1+ sin 0; 19. Four-leaved rose 20. Four-leaved rose r = cos 20; 0 = 0, ±ñ/2, 0 = 0, T r = sin 20; 0 = ±m/4, ±3#/4

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Q: Tangents to Curves

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Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 ln cos t k,     0 ≤ t ≤ π/4

A: Consider the length of the curve is, r(t)=costi+sintj+(lncost)k Then,…

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Q: Consider the curve C shown in the figure, parameterized by: C: r(t) = (1 - cos(t), 1- sin(t), 1 +…

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Q: 5. Find the length of the curve given by x = cos t +t sin t, y = sin t – t cost, -T <t <

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Q: 27. Show that the curve with parametric equations x = t cos t, y =t sin t, z = t lies on the cone z²…

A: To Show: i. Show that the curve with the parametric equationx=tcost, y=tsint, z=t  lies on the…

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A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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A: The solution of above question is written below.

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