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Use differentials to find an approximate value for [tex] \sqrt[3]{65} [/tex]

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Madankapoor10id
: Let y = f(x) =  x^1/3  
Then dy = 1/3*x^(−2/3) dx 
 Since f(64) = 4.
We take x = 64 and dx = ∆x = 1  
This gives dy = 1/3*(64)^(−2/3)* (1) =  1/48  
∴65^(1/3) = f(64 + 1) ≈ f(64) + dy = 4 + 1/48 ≈ 4.021 

Answer:

: Let y = f(x) =  x^1/3  

Then dy = 1/3*x^(−2/3) dx 

 Since f(64) = 4.

We take x = 64 and dx = ∆x = 1  

This gives dy = 1/3*(64)^(−2/3)* (1) =  1/48  

∴65^(1/3) = f(64 + 1) ≈ f(64) + dy = 4 + 1/48 ≈ 4.021 

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