Chapter 7.6, Problem 1MS

Does this thing come with a warranty? If you use two different calculators to do the same calculations, are you guaranteed to always get exactly the same answer? Explain your answer.

To determine

To find:Whether it is guaranteed to get the same answer using two different calculators.

Explanation of Solution

Let there be two calculator, one which rounds it results to eight decimal places and another that truncates it results to eight decimal places.

Now iterate the equation, $y=4x\left(1-x\right)$ on both calculator for $10$ times.

$n$	$x_n$	$x_n{}^{\prime }$
$0$	$0.30000000$	$0.30000000$
$1$	$0.84000000$	$0.84000000$
$2$	$0.53760000$	$0.53760000$
$3$	$0.99434496$	$0.99434496$
$4$	$0.02249224$	$0.02249224$
$5$	$0.08794536$	$0.08794535$
$6$	$0.32084839$	$0.32084836$
$7$	$0.87161880$	$0.87161875$
$8$	$0.44759787$	$0.44759801$
$9$	$0.98901607$	$0.98901612$
$10$	$0.04345313$	$0.04345293$

Table (1)

As the value of $n$ increases the result diverges and if the iteration is increased further, the value changes such that they are no where near each other.

Therefore, it is not guaranteed to get the same result using two different calculator as it can be seen from Table (1), the values diverges as the iteration is increased.