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The derivative of the function AA is given by A′(t)=2+9e0.4sintA′(t)=2+9e0.4sin⁡t, and A(1.2)=7.5A(1.2)=7.5. If the linear approximation to A(t)A(t) at t=1.2t=1.2 is used to estimate A(t)A(t), at what value of tt does the linear approximation estimate that A(t)=15A(t)=15 ?

Respuesta :

sqdancefan

Answer:

  t ≈ 1.697798

Step-by-step explanation:

The linear approximation at t=1.2 is ...

  A ≈ A'(1.2)(t -1.2) +A(1.2)

  ≈ 15.0663(t -1.2) +7.5

We want this to be 15, so we have ...

  15 = 15.0663(t -1.2) +7.5

  7.5/15.0663 = t -1.2 . . . . subtract 7.5, divide by 15.0663

  7.5/15.0663 +1.2 = t ≈ 1.697798

The linear approximation at t = 1.2 is 1.697798.

The linear approximation at t = 1.2 is ...

A ≈ A'(1.2)(t -1.2) +A(1.2)

≈ 15.0663(t -1.2) +7.5

We want this to be 15, so we have ...

15 = 15.0663(t -1.2) +7.5

7.5/15.0663 = t -1.2                 ......subtract 7.5, divide by 15.0663

7.5/15.0663 +1.2 = t ≈ 1.697798

Therefore, The linear approximation at t = 1.2 is 1.697798.

For more information:

https://brainly.com/question/2254269

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