Question No : 29
The solution to the logistic differential equation dy/dx = ky(1 - y) is often used to model population growth. What happens to the population when y = 1?
Question No : 30
If the rate of change of a quantity is given by f'(t) and ?(0 to 4) f'(t) dt = 10, what can you conclude about the quantity at t = 4?
Question No : 31
What is the equation of the tangent plane to the surface z = 2x^2 + 3y^2 at the point (1, -1, 5)?
Question No : 32
A ball is thrown into the air, and its height (in meters) above the ground at time t (in seconds) is given by h(t) = 4.9t^2 + 15t + 2. What is its initial velocity?
Question No : 33
The area between the curve y = x^2 and the x-axis from x = 0 to x = 2 is equal to:
Question No : 34
What is the volume of the region bounded by the surfaces z = x^2 + y^2 and z = 4 - x^2 - y^2?
Question No : 35
What is the derivative of f(x) = 4x^3 - 2x^2 + 5x - 1 with respect to x?