Use differentials to approximate the quantity. (Round your answer to four decimal places.)

Question

Use differentials to approximate the quantity. (Round your answer to four decimal places.)

^3220

Please explain how you obtained the above approximation by answering the following questions.

a)    In order to use the differential, we need a function. What is the most appropriate function for this problem? y = f(x) = 

 

b)    What is the differential of this function? dy = 

 

c)    What is the most appropriate value for x?  (Enter an integer.)

d)    What is the corresponding value of dx? 

e)    What is the corresponding value of dy?  (Round your answer to four decimal places.)

Answer 1

a) y = f(x) = x^1/3

b) dy = dx/(3x^2/3)

c) 220 is close to 6³, so x = 216

d) dx = 220-216 = 4

e) dy = 4/(3(6)²) = 4/108 ≈ 0.0370

Note: y ≈ 216^1/3 + dx = 6.0370

The actual value of 220^1/3 ≈ 6.03681

(6.03681-6.037)/6.03681 ≈-0.0000265 = -0.00265% error. Not too bad.