calculus Q2 (T/F) Determine whether the following statements are true or false.

Question

calculus Q2 (T/F) Determine whether the following statements are true or false. If true. explain your reasoning. If false, provide a counterexample. (a) d/dx(y^2) = 2y. dy/dx(y^2) = 2ydy/dx. Say that you throw a rock upward from the rooftop, and the altitude of the rock is given by the position function s(t) = -16t^2 + 32t + 128. What is the velocity of the rock when it hits the ground? 3. Find the equation of the tangent line of the curve -e^x+y = x/y^3 at the point (1, -1). 4. A spherical ice is melting symmetrically so that the radius is decreasing .1 inch every second. How fast us the volume of the ice decreasing when the radius is 4 inches?

Explanation / Answer

1. a)False.

      d(y2)/dx = 2y x (dy/dx) because y^2 is not a function of x.

   b)false

     dy(y2)/dx = y2 (dy/dx)

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