**Question 1**

Question 2

Question 3

Question 4

Answer to question 1

Answer to question 2

Answer to question 3

The first partial derivatives with respect to x and with respect to y of the surface z=f(x,y) indicate the slopes of the surface in the direction of the x – axis and y – axis respectively.We have the function f(x,y)=4×2+8y2+36. So let’s find its partial derivative with respect to x. Then calculate the partial derivative with respect to x treating y as constant:

Answer to question 4

Observe the graph of the given region Q bounded by the graphs of the equations Q:8x+8y+6z=48,x=0,y=0,z=0

We are required to find the mass and the y – coordinate of the center of mass of the above solid region given that the region has the density ρ ( x , y , z ) = k y where k is a constant.

The mass of the given region is given by the triple integral,