To fix that choose an 'a' that is close to the number you want an estimation. The farther away you go from 'a' the more precision you lose. You see that our estimation is not as precise as the last. The actual answer to five decimal places for (37)^(1/2)=6.08276. Now if we do the same procedure and if we wanted to figure out (37)^(1/2). When you work everything out your L(x)= 5 + (1/10)(x-25) Majority of the time local linearization is only used on points that are close to your original point.
It will all depend on how good of an approximation you want.
The farther away you move from your original point, the more precision you lose.
