calculus Q 1, 2, 3, and 4 (T/F) Determine whether the following statements are t

Question

calculus Q 1, 2, 3, and 4 (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).. d/dx (y2) = 2y

False..

since the given function is in y and we are differentiating this with respect to x.

counter example:    d/dy (y2) = 2y

(b) dy/dx (y2) = 2y (dy/dx)

False

counter example :   (dy/dx) (d/dy)(y2) = 2y (dy/dx)

or

d/dx (y2) = 2y dy/dx

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