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satela [25.4K]
3 years ago
14

D. Direction: Plot following irrational numbers in the given number line.

Mathematics
1 answer:
Tju [1.3M]3 years ago
8 0

Answer:

<u>Numbers and plot location given below:</u>

<u />

  1. √15 = 3.9  located between 3.8 and 4.0
  2. √46 = 6.8 located between 6.7 and 6.9
  3. √55 = 7.4 located between 7.3 and 7.5
  4. √60 = 7.7 located between 7.6 and 7.8
  5. √96 = 9.8 located between 9.7 and 9.9
  6. √14 = 3.7 located between 3.6 and 3.9
  7. √22 = 4.7 located between 4.6 and 4.8
  8. √75 = 8.7 located between 8.6 and 8.9
  9. √34 = 5.8 located between 5.7 and 5.9
  10. √57 = 7.5 locate between 7.4 and 7.6
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Video Example EXAMPLE 1 Find the linearization of the function f(x) = x + 1 at a = 3 and use it to approximate the numbers 3.98
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Answer:

  the linearization is y = 1/4x +5/4

  the linearization will produce <em>overestimates</em>

  the values computed from this linearization are ...

     f(3.98) ≈ 2.245

     f(4.05) ≈ 2.2625

Step-by-step explanation:

Apparently, you have ...

  f(x)=\sqrt{x+1}

from which you have correctly determined that ...

  f'(x)=\dfrac{1}{2\sqrt{x+1}}

so that f(3) = 2 and f'(3) = 1/4. Putting these values into the point-slope form of the equation of a line, we get the linearization ...

  g(x) = (1/4)(x -3) +2

  g(x) = (1/4)x +5/4

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The values from this linearization will be overestimates, as the curve f(x) is concave downward everywhere. The tangent (linearization) is necessarily above the curve everywhere.

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At the given values, we find ...

  g(3.98) = 2.245

  g(4.05) = 2.2625

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