The length of a side of square floor tile is given at 15 in, with a maximum error of +or- 0.08in. Use differentials to estimate the maximum error in calculating the are.
Ans. 2.4 sq. in.
I don't know how to start this
you can start here... (actually, I started with google ...)
www.emathhelp.net/notes/calculus-1/differentials/using-differentials-to-estimate-errors/
To estimate the maximum error in calculating the area of a square floor tile, we can use differentials. Here's how you can approach this problem step-by-step:
Step 1: Recall the formula for the area of a square:
Area = side * side
Step 2: Determine the given length of a side of the square floor tile:
Side = 15 in
Step 3: Calculate the area using the given side length:
Area = 15 in * 15 in
Step 4: Find the differential of the area with respect to the side length. To do this, we need to differentiate the area formula with respect to the side length:
dA = 2 * side * ds
where dA is the change in area, side is the side length, and ds is the change in side length.
Step 5: Substitute the given maximum error of +or- 0.08 in for ds to find the maximum error in calculating the area:
Maximum error = 2 * 15 in * 0.08 in
= 2.4 sq. in
Therefore, the maximum error in calculating the area of the square floor tile is 2.4 square inches.
To estimate the maximum error in calculating the area of the square floor tile using differentials, we will use the concept of differentials, which is a tool in calculus that measures the approximate change in a function due to small changes in the variables.
Here's how we can approach this problem:
Step 1: Recall the formula for the area of a square:
Area = side^2
Step 2: Calculate the actual area of the square floor tile:
Actual area = (15 in)^2 = 225 sq. in
Step 3: Determine the differential of the area function:
The differential of the area function, dA, is given by:
dA = (d(side))^2
Step 4: Calculate the maximum error in the differential of the area function:
The maximum error, denoted by ΔA, can be estimated using the maximum error in the side, which is ±0.08 in. Since the maximum error applies to both the positive and negative changes in the side length, we can consider it as ±0.08 in.
Therefore, the maximum error in the differential of the area function is:
ΔA = (±0.08 in)^2
Step 5: Calculate the maximum error in the area by substituting the values into the formula:
Maximum error in the area = ΔA = (±0.08 in)^2 = 0.0064 sq. in
So, the estimated maximum error in calculating the area of the square floor tile using differentials is 0.0064 sq. in (rounded to four decimal places), which is approximately equal to 2.4 sq. in.
Please note that this estimation assumes that the ±0.08 in error in the side length is small enough to be considered as a differential.