Anonymous asked in Science & MathematicsMathematics · 1 month ago

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 : ?



Attachment image

1 Answer

  • Ian H
    Lv 7
    1 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

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