Problem VII: Evaluate ye"dx +xe"dywhere C is the portion of the curve y = x' - x² +1 from (0, 1) to (1, 1).

3. When origin shifted to the point (2,3), the transformed equation of the curve is x² + 3xy – 2y2 + 17x – 17y – 11 = 0. Find the original equation of the curve?

25. Consider the curve defined by the equation below and a point (2, 1) on the curve. What is the equation of the tangent line at the point (2, 1)? x? - 3y = 1 4х — Зу- 5 %3D 0 4x – 3y + 2 = 0 2х — 3у - 1 %3 0 4х — 3у + 5 %3 0 |

Problem X: Evaluate [(x In y+ y)dx +(x+1+ -)dy where C is the portion of the curve 2y y =x' - x² +4 from (0, 4) to (2, 8).

1. Let C' be the curve described by the equation ³ + 3x²y - xy² = 3. dy da (b) C contains the point (-1,1). Find the two other points at which C intersects the line y = 1. Note: your final answers should be in the form (x, 1). (c) Find the equations of the lines tangent to C at each of the three points in part (b). (a) Find 2. Find the indicated derivatives. dy (a) y = π 3 (cos(x) + 2)", dx ds (b) 2st2 + cos(3s +t)=√s-1, dt 3. When asked to determine the derivative for the function f(t) = (csc² (t))", one student provided the following solution: f' (t) = π (csc² (t))" (2-csc(t)) (-csc(t) cot(t)) (a) What error(s) did the student make while attempting to find f'? Identify the error(s) and provide an explanation that you would use to correct the student's thinking. That is, your explanation should help the student avoid making the same mistake on future problems. (b) Determine the correct derivative for the function f(t) = (csc² (t))**.

44)

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.