1.15: Past-paper question 10

(a) Expand simplifying each $\displaystyle -$ term in ascending as far as possible. powers of $\displaystyle x$ up to and including the term in $\displaystyle X^{3},$

(b) Write down the range of values of $\displaystyle x$ for which your expansion is valid.

(c) term Find in the series simplifying expansion each of term f(x) in as ascending far as possible. powers of $\displaystyle x$ up to and including the

The positive region y-axis is and bounded the line by with the curve equation with equation $\displaystyle y =$ f(x), the positive x-axis, the

(d) Using of giving your expansion your answer of f(x) to and decimal algebraic places. integration, find an estimate for the area