Question 1

(i)

(ii)

Using long division, we find that

So the asymptotes are and

Question 2

(i)

This is a hyperbola with centre , asymptotes are , and vertices and .

is a graph with asymptotes and .

Use GC to plot.

(ii)

—(1)

—(2)

Subst (2) to (1),

(iii)

From graph, we observe two intersections. Thus, two roots.

Question 3

(ai)

(aii)

(bi)

Let

Let

(bii)

(biii)

As , and , the sum of series tends to , a constant. Thus, series is convergent.

(biv)

Replace by . Then we have