Calculus Questions (Integrals, Linear approximations and Differentials)?
Please show detailed steps. Thanks a lot in advance :)
The picture below is Question 1.
Question 2: The radius of a sphere is measured to be 7 mm with the accuracy of 0.5 mm :
a) Estimate the propagated error in the surface area of the sphere. (Round your answer to two decimal places)
Ans: dA = ± ?
b) Compute the surface area of the sphere if the radius is (i) 6.95 mm and (ii) 7.05 mm and find the actual error of measurement.
[The surface area of a sphere is A = 4𝜋r^2 where r is the radius of the sphere)
Hint for b : The actual error is in the format E1 ≤ dA ≤ E2
If your answer is negative, enter a negative number
Round your answer to two decimal places
Ans: value of E1 : ?
value of E2 : ?
- Ian HLv 71 month ago
A = 4πr^2
dA/dr = 8πr
dA = 8πrdr = 8π*7*0.5
dA ~ ± 87.9646...
Substituting 7.5 and 6.5 into A gives
max value 706.858
min value 530.929
The difference/2 = dA