Suppose F(x, y) = −y sin(x)i + cos(x)}. (a) Find a vector parametric equation for the parabola y = x² from the origin to the point (2, 4) using t as a parameter. r(t) = (b) Find the line integral of F along the parabola y = x² from the origin to (2, 4).

The curve in the plane defined by the equation (*) (x^2 + xy + y^2 = 7) is a rotated ellipse, shown in the figure. a) Use implicit derivation to find dy/dx expressed by x and y. (b) Show that the curve passes through the point (2,1) and find the equation of the tangent line to the curve at the point (2,1).

است awat parametric Diffi dy(x) dx x- - 2 Cos (2+) Y= 6 sin (+) السلام