Please solve all problems with work:

1. Find by implicit differentiation and simplify: x = sin (x + y). Show the work that leads to your answer. Leave your answer with no negative exponents and as a single rational function, if applicable. 2. Consider the closed curve in the xy-plane given by x2 + 2x + y* + 4y = 5. (a) Find " and simplify. Show the work that leads to your answer. Leave your answer with no negative exponents and as a single rational function, if applicable. (b) Find the coordinates of the two points on the curve where the line tangent to the curve is vertical. Show the work that leads to your answer. 3. Given the curve x2/3 + y2/3 = 5. (a) Find the equation of the line tangent to the curve at the point (8,1). Show the work that leads to your answer. (b) Find the equation of the line normal to the curve at the point (8,1). Show the work that leads to your