please answer from your own work on a paper providing all steps for good feedback.

1. To pammeten'ze a curve is to represent it with parametric equations. There are usually man}; wan a curve can be parameterized. Find one correct parameterization for each curve below. a] The parabola y 2 3x2. b] The unit circle. c] The right triangle with vertices (D. D], (D, 1). and [1, ). traced out with a counterclockwise orientation, beginning and ending with (D, Ill). d] The square with vertices {2. 2], (2,2),{2, 2], and (2, 2], traced out with a clockwise orientation. beginning and ending with (2, 2). 2. Use these steps to sketch the curve with equations x = t2, 3;: = t3 St. a] Find (3:de and use it to show that the curve has two tangent lines at the point [3, Ill}. b] Set :13:de equal to zero to nd where the curve is horizontal. c] Discover where dyfdx is undened [nonzerofzero] to nd where the curve is vertical. d] Find dzyfdxz and use it to determine where the curve is concave upward or downward. e] Sketch the curve. 3. Find the slope of the line tangent to the curve 3: = 1 + In t. y = t2 + 2 at the point (1. 3] using two methodsrst without eliminating the parameter, then by eliminating the parameter. a] Express dyfdx in terms of t. Substitute the correct number for t to nd the slope at (1.. 3]. b] Solve for t in terms of 1:. Use this to express I in terms of 3:. Find the slope at {1. 3]. c] Write the equation of this tangent line