Task 2 Expand (2x+3y)5 using Pascal’s triangle.
Use the binomial theorem to expand √(4+x) in ascending powers of x to four terms.
Use the binomial theorem to determine, correct to 4 decimal places:
(a) (1.003)8 (b) (0.98)7
4. The energy W stored in a flywheel is given by:
W =kr5N2, where k is a constant, r is the radius and N the number of revolutions.
Determine the approximate percentage change in W when r is increased by 1.3% and N is decreased by 2%.
Task 3 Use the Taylor series centred around a=0 to write the first four terms of the expansion of f(x) = 1/(1+x) and hence write its general formula.
A. Write down the first four terms of the Maclaurin expansion for f(x)=ex.
B. Calculate the sum of the first four terms of the expansion of f(x) = ex, for x = 1.
C. Compare your result with the value for e1 obtained from your calculator.
Checklist of evidence required Your informal report should contain the worked solutions to the problems using the values given to you by your tutor. Each worked solution should be laid out clearly and contain brief explanations of the stages of the calculation to indicate your understanding of the subject. Diagrams should be well presented and clearly labelled.
Criteria covered by this task:
Unit/Criteria reference To achieve the criteria, you must show that you are able to:
8/A.D1
Evaluate, using technically correct language and a logical structure, engineering problems using non-routine sequence and series operations, while solving all the given problems accurately using routine and non-routine operations.
8/A.M1 Solve given problems accurately using routine and non-routine arithmetic and geometric progression operations.
8/A.M2 Solve given problems accurately using routine and non-routine power series operations.
8/A.P1 Solve given problems using routine arithmetic and geometric progression operations.
8/A.P2 Solve given problems using routine power series operations.