Patrick F. answered • 10/12/23
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Washington H.
asked • 10/11/23AP Calculus BC - Linearization
Find the linearization of the given function centered at x = a, use it to estimate f(b).
f(x) = sqrt(17 sin(x)), a = π/6, b = 0.5
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Yefim S. answered • 10/12/23
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f(x) = √(17sinx); f(π/6) = √8.5; f'(x) = √17cosx/(2√sinx); f'(π/6) = √17·(√3/2)/(√2) = √102/4
L(x) = √8.5 + √102/4(x - π/6)
f(0.5) ≈ L(0.5) = √8.5 + √102/4(0.5 - π/6) = 2.97506
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Patrick F.
Please note: There is a calculation error at the very end. Should be approximately 2.85610/12/23