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

: 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

Answered by madankapoor10 | 2024-06-10

: 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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Answered by 123bryantelleriasrij | 2024-06-12

We used differentials to approximate 3 65 ​ . Starting from the known cube root of 64, we found the derivative and calculated the difference to estimate the value. The approximation yields 3 65 ​ ≈ 4.021 .
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Answered by madankapoor10 | 2024-10-01