Computational Physics Questions ( Maple )
1). Numerically evaluate giving your answer to 16 significant figures.
(2). What is the 300’th digit in ?
(3). Evaluate
(4). Evaluate .
(5). (a) Which Maple command calculates a random integer?
(b) How might you use it to calculate a random decimal number between 0 and 1 with 3 significant figures.
(6). Find the following limit:
(7). Evaluate
(8). Write down the Maple commands which would produce a function which is the Taylor series
approximating the function up to third order about x=0, and then plot both the original function
and the approximation on the same plot, for x in the range 0 to .
(9). In section 4.1 of the worksheet you were asked to determine what value in the series command yielded an
approximation accurate to 9 decimal places. What value did you find?
(10). Define the function
Using a loop, evaluate using different numbers of significant figures of accuracy (as controlled by
the value of Digits – see section 2) in the range 5 to 30. What do you find? Can you get Maple to evaluate
exactly? What is the exact value of , and how does it compare to the values generated in your loop.