Use a parameterization of the lower portion cut from the sphere x squared plus y squared plus z squared equals 4x2+y2+z2=4 by the conez equals startfraction 1 over startroot 3 endroot endfraction startroot x squared plus y squared endrootz=13x2+y2 to express the area of the surface as a double integral. then evaluate the integral.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).