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Question: consider a plane curve c given by the parametric equations...

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Consider a plane curve C given by the parametric equations x(t) = 6t2 and y(t) = 3t3 − 4t. Note: In the solution of this problem use symmetry wherever possible.

  1. (a) Find the point A(x0,y0) where C crosses itself. Hint: Solve the system of equations 6t21 = 6t22 and 3t31 − 4t1 = 3t32 − 4t2.

  2. (b) Find equations of both tangents at A.

  3. (c) Find the points on C where tangent is horizontal or vertical.

  4. (d) Determine where C is concave upward or downward.

  5. (e) Indicate by arrows the direction of C.

  6. (f) Find the area enclosed by the loop. Hint: Look at the problem 77 in the section 10.3

    of the textbook. Note: If you integrate the loop counterclockwise, the integral will be

    negative. Take absolute value of your answer.

  7. (g) Find the arc length of the loop.

(4) Consider a plane curve C given by the parametric equations () 62 and y(t) 3t3 -4t. Note: In the solution of this problem

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