Question

using differentials,find the approximate value of (17/18)¼​

please fast answer guyzz

Answer 1

Answer:

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Step-by-step explanation:

[17/81]^4 = 174 / 814 = 174/3

let f(x) = x4

f'(x) = 1/(4x4).

now,

{f(x + Ax) - f(x)} = f'(x)*Ax

{f(x + Ax) - f(x) = 1/(4x4)*Ax------( 1)

we may write 17 = (16 + 1). putting x = 16 , Ax = 1 ----- in ---(1)

we get,

f(16 + 1) f(16) = 1/4(16)4 * 1

f(17) - f(16) = 1/4(2®) = 1/32 =

f(17) = 1/32 + f(16)

f(17) = 1/32 + (16)4)

f(17) = 0.03125 + 2

f(17) = 2.03125

(17)4 = 2.03125

approximate value of [17/81]¼ = 2.03125/3

= 0.677