1.

(a) Let r> 0 be a given constant. Consider the function f(x) = √√r² - x² for −r ≤ x ≤ r

and sketch its graph. By considering the body of revolution obtained by rotating the graph

around the x-axis and using an integral, recover the expression for the volume of a sphere

of radius r.

(b) Let us consider the sequence (an) defined by ao = 1, a₁ = -1 and

-1

9an-2 +6

an

What is the value of l?

for n ≥ 2.

MATH19682

Write down the first 5 terms of the sequence.

We will now assume that the sequence is convergent. In other words, we assume that there

exists a finite real number & such that

lim an = l.

n-x

[5 marks]

[5 marks]

[Total: 10 marks]