QUESTION 5 Calculate F.dr if F=(sinx,x²y³) and C is the triangle oriented counterclockwise with vertices at (0,0), (1,0), and (1,1).

Question 2. 1. Find the tangent plane equation and the normal unit vector of the sur- face z = x² + y² at the point (1,-1,2).

EXERCISE 2.2 An automobile follows a circular road whose radius is 50 m. Let x and y respectively denote the eastern and northern directions, with origin at the center of the circle. Suppose the vehicle starts from rest at x = 50 m heading north, and its speed depends on the distance s it travels according to v=0.5s-0.0025s², where s is measured in meters and v is in meters per second. It is known that the tires will begin to skid when the total acceleration of the vehicle is 0.6g. Where will the automobile be and how fast will it be going when it begins to skid? Describe the position in terms of the angle of the radial line relative to the x axis.

Parametrize the intersection of the surfaces y² - z² = x - 6, y² + z² = 25 using trigonometric functions. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give the parametrization of the y variable in the form a cos (t).) x(t) = y(t) = z(t) =