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Sketch the trace of the following curve on R²,
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(t) = (t2 sin(t), t2 cos(t)),
tЄ
22
[3 Marks]
Find the length of this curve.
[7 Marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd66c7573-6777-48ff-9bfb-9b3df1a769a6%2F8d5d1e31-260b-4be1-bfb8-30b634197fc4%2Fvhovv1d_processed.jpeg&w=3840&q=75)
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- Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.Find the slope of the tangent line to the polar curver = 2 sin(36) at the point corresponding to 6 = x/4. Show all work.1. a) Find dy for the equation 4x²y² - x³y=3 dx b) find the x-coordinate of each point on the curve where the tangent line is vertical () Find the y-coordinate of each point on the curve. with an x-coordinate of -1.
- 4. Consider the curve defined by 2x - cot(y) = 5. Which of the following is an expression for the slope of the curve at any point on the curve? (A) (4x-5) sin “(y) (B) –4x sin (jy) (C) 4x cos (y) (D) -4x csc(y) cot (y)2. (i) Describe with a sketch the trace of the following curve in R² (t) = (t² sin(t), t2 cos(t)), (€ -2,2]). [15 Marks] (ii) Find the length of this curve. [25 Marks]Graph the curve x = cos t + 2 cos 2t y = sin t + 2 sin 2t to discover where it crosses itself. Then find equations of both tangents at that point.