Question $4(3$ points$)$

In class we discussed Heron's Method and how to derive it from Newton's method.

Derive a recurrence relation using Newton's Method which iteratively calculates

$(\backslash$sqrt$($x$))/(7)$

What is the recurrence relation?

a$\_($n$)=$a$\_($n$-1)-(49)/(2)($a$\_($n$-1)-($x$)/($a$\_($n$-1)))$

a$\_($n$)=$a$\_($n$-1)-(1)/(2)($a$\_($n$-1)-($x$)/(49$a$\_($n$-1)))$

a$\_($n$)=$a$\_($n$-1)-(1)/(2)($a$\_($n$-1)-($x$)/($a$\_($n$-1)))$

a$\_($n$)=$a$\_($n$-1)-(1)/(2)($a$\_($n$-1)-(7$x$)/($a$\_($n$-1)))$