: 1. Acurve Cisgivenparametricallyas C: 221:2 ;1t2 (a) Use the given parametric equations to in the table of values below and sketch the curve ; scale the axes based on your values. (b) Compute the slope of the tangent line to the curve at t = 1 ; sketch this tangent line on your graph in part (a). (c) Compute the area under the curve ( and above the x-axis ) from t = 0 to t = 2 by evaluating a parametric integral; start by determining the parametric formula for dA.2. A rabbit and a fox travel on paths given parametrically by: x = sin t x =t-2 Rabbit : Fox : Oct 2 = = COS ("t) 1-t with x and y measured in feet and tin seconds. (a) Eliminate the parameter from each pair of parametric equations to identify (state the name of ) each path.(b) Fill in the table below and sketch each path using appropriate selling of the axes; label which is which. What happens at t = 2 ? (c) Com aum the speeds of the fox and the rabbit at t 2 sec. (Please label which 15 3. Given the polar equation: 1' = 4n" 23 (a) Complete the table of values and sketch the curve; show scale on axes. (1}) Compute the slope ofthe tangent line to the curve in part (a) at 3 = g ; sketch this tangent line on your graph. (c) Compute the area enclosed by the graph in part (a) as a polar integral