For the function f(x, y) = (4 - x² - y²), find a unit tangent vector to the level curve at the point (-1,-3) that has a positive a component.

Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

Velocity at the Equator Assuming the radius of the earth is 4,000 miles, use the information from Problem 43 to find the linear velocity of a person standing on the equator.

a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t, where x is the horizontal direction and y is the upward direction. the projectile lands after  a. 16 seconds b. 8 seconds c. 4seconds