# 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 : ?

URGENTTTT!!

### 1 Answer

- 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