Find the linear approximation of the function f(x)=\sqrt{4-x} at a=0

oliviayychengwh 2021-12-18 Answered
Find the linear approximation of the function f(x)=4x at a=0 and use it to approximate the numbers 3.9 and 3.99, please.
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Expert Answer

enhebrevz
Answered 2021-12-19 Author has 25 answers
Use the Taylor Form: f(x)=f(a)+(xa)×f(a)
f(x)=(4x)=12×14x
f(0)=40=2
f(0)=12×14=14
3.9=f(x)2+0.1(14)=1.9750
3.99=f(x)2+0.01(14)=1.9975

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