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Sidana [21]
3 years ago
6

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

and 4.05 . Are these approximations overestimates or underestimates? SOLUTION The derivative of f(x) = (x + 1)1/2 is f '(x) = Correct: Your answer is correct. . and so we have f(3) = 2 Correct: Your answer is correct. and f '(3) = 1/4 Correct: Your answer is correct. . Putting these values into this equation, we see that the linearization is

Mathematics
1 answer:
Blizzard [7]3 years ago
4 0

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

__

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.

__

At the given values, we find ...

  g(3.98) = 2.245

  g(4.05) = 2.2625

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2 years ago
What is 22.5 as a fraction in simplest form
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What is the slope-intercept form equation for the points (10,4) and (10,-5)
scZoUnD [109]

Answer:

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Step-by-step explanation:

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3 years ago
How do I do this problem??
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Expanding 8x^3, we multiply 8*8 and x^3 by x^3 to get 64x^6. Since we know that the cube root of 64 is 4, we can separate that. Next, since you add exponents while multiplying, 6/3 is the exponent for the cube root of x^6=x^2. Therefore, your answer is 4x^2
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How do you solve <br> -178=-5x+4(-4x-13)
Effectus [21]

Answer:

x = 6

Step-by-step explanation:

  • <em><u>Pull out like factors: </u></em>

-4x - 13  =   -1 • (4x + 13)

  • <em><u>Equation at the end of step 2: </u></em>

 -178 -  (-5x +  -4 • [4x + 13] )  = 0

  • <em><u>Pull out like factors: </u></em>

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  • <em><u>Equation at the end of step 4: </u></em>

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x-6 = 0  

  • <em><u>Add 6 to both sides of the equation:</u></em>

x = 6

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3 years ago
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