Iff(x) = 3 cos2(x),compute its differential df.df =  Approximate the change in f when x changes fromx = π6tox = π6 + 0.1.(Round your answer to three decimal places.)Δf ≈  Approximate the relative change in f as x undergoes this change. (Round your answer to three decimal places.)

Question
Asked Nov 13, 2019
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If
f(x) = 3 cos2(x),
compute its differential df.
df =
 
 
Approximate the change in f when x changes from
x = 
π
6
to
x = 
π
6
 + 0.1.
(Round your answer to three decimal places.)
Δf ≈
 
 
Approximate the relative change in f as x undergoes this change. (Round your answer to three decimal places.)
 
 
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Expert Answer

Step 1

Compute the differentials, df.

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f(x)=3cos2x Differentiate fwith respect to x,

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Step 2

Apply the chain rule,

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df (u)_df du dx Let, f2ucos.x df (2 )(-sin x) dx df 3(2c0s.x)(-sin x) dx df-3(2 cos.x)(sin x)cr df-3sin2x)dx

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Step 3

From the condition w...

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Thus, x changes from " to- +0.1 6 Ax =+0.1-"=0.1 6 and Ar 0.1 Where, x 6

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Tagged in

Math

Calculus

Derivative