Algebra

mpx

drawing

Write as partial fractions.
(a) Expand in ascending powers of up to and including the term in , stating the range for which the expansion is valid.
(b) Use this expansion to calculate correct to 4 decimal places.
The function f is given by

(a) Write

as a sum of two partial fractions.
(b) Expand your fractions to find a quadratic approximation to

.

Explain why your expansion will not give a valid approximation to

.
4. Given that

, find the values of

and

.
5. (a) Expand

up to and including the term in

.
(b) Mo uses the expansion from part (a) and the value

to find a value for

. Find Mo’s result and explain why this is not a valid approximation.

Use the expansion from part (a) to find a value for

to 2 decimal places and explain why this is a valid approximation.
(d) Use your result from

to find a value for

correct to 2 decimal places.
6.

is approximately equal to

(a) Find the values of

and

.
(b) Emily wants to use this expansion to calculate an approximation for

.

Give one reason why using this expansion would not give a valid approximation.
7. (a) Write

as partial fractions.
(b) Find the

coordinate(s) of any turning points on the curve

and identify their nature.

drawing