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natulia [17]
3 years ago
8

(a) Write the equation of the line that represents the linear approximation to the following function at the given point a. (b)

Use the linear approximation to estimate the given quantity. (c) Compute the percent error in the​ approximation, 100 * [ | approximation - exact | Over | exact | ], where the exact value is given by a calculator. f (x)= 3 - 3 x² at a = 1​; ​f(0.9​)

Mathematics
1 answer:
Elza [17]3 years ago
3 0

Answer:

  (a) y = -6(x -1)

  (b) about 5.3%

Step-by-step explanation:

(a) The point used as the base for the linear approximation is (1, f(1)), where ...

  f(1) = 3 -3·1² = 0

The slope of the line at that point is ...

  f'(x) = 0 -3(2x) = -6x

  f'(1) = -6·1 = -6

So, in point-slope form, the equation of the approximating line is ...

  y = -6(x -1) +0

  y = -6(x -1)

__

(b) The approximate value of f(0.9) is then ...

  y = -6(0.9 -1) = 0.6 . . . . approximate value of f(0.9)

__

(c) The error in the approximation at x=0.9 is ...

  error% = (0.6 -f(0.9))/f(0.9) × 100%

where f(0.9) = 3(1 -0.9²) = 3·0.19 = 0.57

  error% = (0.6 -0.57)/0.57 × 100% = 0.03/0.57 × 100%

  error% ≈ 5.263% ≈ 5.3%

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Answer:

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3 0
3 years ago
Please do correctly! I will mark you Brainliest!
kolbaska11 [484]

Answer:

3(4+√2)

Step-by-step explanation:

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3 years ago
Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were all
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Let events
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T=Nathan tests positive
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We are given
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We want to calculate probability that Nathan is allergic AND tests positive
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3 years ago
Louann and Carla received equal scores on a test made up of multiple choice questions and an essay. Louann got 14 multiple choic
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So 6 didn't work and you already should know that the answers should be between 1 and 5. 

So now I going to do 5 for x
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7 0
3 years ago
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