- 1)
- a)
- (2 pts) Compute the relative error in the
expression 1-
*x*^{4}when*x*=1.01. Use 3 digit, rounded arithmetic. - b)
- (2 pts) Repeat a) using the equivalent expression
(1-
*x*^{2})(1+*x*^{2}). Which expression is more accurate? - c)
- (2 pts) Modify the expression in b) to obtain an expression that is even more accurate. Compute the resulting relative error.

*x*^{4}.- 2)
- Each of the expressions below will suffer from catastrophic
cancellation error for the given ranges of
*x*. Rewrite the expressions so that catastrophic cancellation does not occur.- a)
- (1 pt)
for
*x*large - b)
- (2 pt) for
- c)
- (2 pt) for (HINT: Use the difference of 2 cubes).

2017-09-01