Change sqrt (including its Javadoc comments) so it also works when x = 0. Note: if your code from Newton1 appears to work without any changes, but it is such that it might execute a division by 0, then it is not correct. Division by 0, in general, is undefined and you should not write code that attempts to compute it.
Question
Change sqrt (including its Javadoc comments) so it also works when x = 0. Note: if your code from Newton1 appears to work without any changes, but it is such that it might execute a division by 0, then it is not correct. Division by 0, in general, is undefined and you should not write code that attempts to compute it.
Solution
Sure, to make the sqrt method work when x = 0, we need to add a condition at the beginning of the method to check if x is zero. If x is zero, the method should immediately return 0 as the square root of 0 is 0. This will prevent any division by zero errors in the subsequent calculations.
Here's how you can modify the sqrt method:
/**
* Computes estimate of square root of x to within relative error 0.01%.
*
* @param x
* non-negative number to compute square root of
* @return estimate of square root
*/
private static double sqrt(double x) {
if (x == 0) {
return 0; // The square root of 0 is 0
}
double guess = x; // Initial guess is set to x
while (Math.abs(guess * guess - x) / x >= 0.0001) {
guess = (guess + x / guess) / 2; // Update the guess using Newton's iteration formula
}
return guess; // Return the estimated square root
}
In this updated implementation, the sqrt method first checks if x is 0. If x is 0, the method immediately returns 0. Otherwise, it proceeds with the Newton's iteration method to estimate the square root of x with a relative error of 0.01%.
Also, note that I've updated the Javadoc comment to specify that x should be a non-negative number, as the square root is undefined for negative numbers.
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