1 Consider the expression 1/(1 + ε)3

a) Show that this expression is approximately equal to 1−3ε plus terms in ε2 and higher orders.

b) Compute the precision of the approximation neglecting the higher order terms for the cases of ε = 0.007 and ε= 0.7. Precision in this case means the absolute value of the difference between the approximation and the full result, divided by the full result.

c) Suppose you are doing a problem in which the input values are given to you to a precision of two decimal places, as is often the case in this course. For what values of ε is it appropriate to use the first order approximation for 1/(1 + ε) 3 ?