Question 11
The volume of a cone can be determined by summing up the infinitesimal circular cross-sections of the cone across the length of the cone Consider the function f(x) = x2 for x contained in [0,1].
Now consider an infinitesimal circular cross-sectional element of width dx and radius r = f(x) Determine the volume of the cone enclosedby the function f(x) by considering the volume of each circular cross-sectional element (Recall thatthe sum of infinitesimal elements can be represented as an integral Recall also that the area of a
circle is
A)
B)
C)
D)
1
Question 12
Identify which of the following statements is not true.
Question 13
Consider the following definite integral:
Determine for which combination of a and b the integral converges.
A)
B)
C)
D)
Question 14
In an Olympic Race there are 100 competitors.
Calculate the number of ways of distributing the Gold. Silver and Bronze medals amongst all of the competitors.
A)
B)
C)
D)
Question 15
A snack bar does not give an itemised bill tor drinks In the past three visits, the total bills have been:
1) Three teas, two coffees and one lemonade cost £9.80
2) One tea four coffees and two lemonades cost £13.60
3) Two teas, two coffees andtwo lemonades cost£10
Calculate the price for a single coffee, given the prices have been the same for the three visits.