Chapter 2.4, Problem 43E

The correct answer is D Could you please explain why

For number 4 the answer is B Could you explain why

The answer is C Could you explain

Use the shell method to find the volume of the solid generated by revolving the region bounded by x = 3√y, x = -y, and y = 2 about the x-axis.

The answer is A Show me how to do it

For number 9 The answer is A Could you show me how

The answer is B, Could you please show the steps to obtain the answer

2. Suppose that U(x, y, z) = x² + y²+ z² represents the temperature of a 3-dimensional solid object at any point (x, y, z). Then F(x, y, z) = -KVU (x, y, z) represents the heat flow at (x, y, z) where K > 0 is called the conductivity constant and the negative sign indicates that the heat moves from higher temperature region into lower temperature region. Answer the following questions. (A) [90%] Compute the inward heat flux (i.e., the inward flux of F) across the surface z = 1 - x² - y². (B) [10%] Use the differential operator(s) to determine if the heat flow is rotational or irrotational.

Could you show why the answer is B Using polar coordinates and the area formula