Differential Application Problem?

Question

I believe I did this problem right, but I would just like someone to confirm if it is right. Here is the question:

About how accurately should you measure the side of a square to be sure of calculating the area within 2% of it's original value?

A = S^2

dA = 2S dS

dA
(
dA
dA
2SdS
The S cancels with the S^2, so:

2dS
dS
Thus, I said the side of a square must be measured with a 1/100, or 1%, accuracy to be able to calculate the area within 2% of its original value.

Answer 1

A = S^2 (1)
dA = 2S dS (2)
& dA
from (1) & (3) & simple mathematics calculation;
►dA
from (2)
2S dS
dS
►► dS

So you are right;

.

Answer 2

Yes its correct
S = x^2
S + dS = (x+dx)^2 = x^2 + 2xdx + (dx)^2
dS = 2xdx [ignoring (dx) ^2]
ds/S = 2 dx/x
but we know 2dx/x <= 0.02
dx/x <= 0.01
Answer is 1%

Answer 3

from my view if u ask i think its correct bcoz the formula u r using is correct.

Answer 4

No!
Please give me best answer thanks!