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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

You might be interested in
Please help me with 9 I really need it
MissTica

Answer:

605 boys

Step-by-step explanation:

If the ratio of boys to girls is 5:7

and there are 847 girls

we can plug this value into the ratio by doing something like:

5:7

= 5/7

= x/847

Because the ratio has to be the same, we can substitute x for the number of boys and solve by the cross method or whatever you guys call it.

5            x

---   x    ------

7          847

The x in the middle is just to show the direction you are multiplying.

the 5 is multiplied by the 847 and the 7 is multiplied by x.

847 * 5 = 4,235

4,235  divided by 7 is 605

605 is your answer.

The cross method can be used in most situations.

* is used to represent multiplication btw

4 0
2 years ago
1st question: Reuben received 80 dollars. Write a signed number to represent this change.
lesya692 [45]

Answer:

1) +80

2) -1520

Step-by-step explanation:

Positive Signed numbers are used in real world situations to indicate the increase. Examples include; increase in weight, deposit of money into an account, increase in income, profit, height above sea level, etc. They are all represented by positive signed numbers.

Whereas, negative signed numbers show decrease. Examples include; loss of weight, withdrawal of money from an account, loans, liabilities, losses, temperature below zero degrees, height below sea level.

1) We are told that Reuben received 80 dollars. Thus, it means he received an increase in the amount of money he already had. Thus, the signed number will be +80.

2) We are told that A car corporation produced 1520 fewer cars this month than last.

Thus, the signed number will be negative since there is a decrease in number of cars.

Thus, signed number = -1520

7 0
2 years ago
Is the following relation a function?<br><br> x y<br> −1 −2<br> 2 3<br> 3 1<br> 6 −2
PilotLPTM [1.2K]
Yes because no same x-valu resulted in different y-values.
6 0
3 years ago
Read 2 more answers
For breakfast, Sarah can choose eggs, granola or oatmeal as a main course, and orange juice or milk for a drink. Sarah says that
svlad2 [7]

Answer:

The explanation is given below

Step-by-step explanation:

Her error is that she multiplied the possibilities of her meal that involves eggs with milk, granola & oatmeal but the possibilities involves orange juice with egg and granola & oatmeal

Now

If she choose milk so she can select eggs, granola, and oatmeal so there are 3 possibilities also with the orange juice there is 3 possibilities

So, the sample space is

= 3 + 3

= 6 outcomes  

4 0
2 years ago
According to a Gallup survey conducted in July 2011, 20% of Americans favor reducing the U.S. budget deficit by using spending c
Yakvenalex [24]

Answer:

Option C is correct.

The test statistic for this question is -3.13

Step-by-step explanation:

To compute the z-test statistic, the formula is given as

z = (x - μ₀)/σₓ

x = p = sample proportion of the 500 college students sampled, that favor reducing the deficit using only spending cuts with no tax increase = (75/500) = 0.15

μ₀ = p₀ = the proportion to be compared against, that is, the proportion of Americans that favor reducing the U.S. budget deficit by using spending cuts only, with no tax increases = 20% = 0.20

σₓ = standard error of the sample proportion = √[p(1-p)/n]

p = 0.15

n = Sample size = 500

σₓ = √[0.15×0.85/500] = 0.01597

z = (0.15 - 0.20) ÷ 0.01597

z = -3.13

Hope this Helps!!!

8 0
3 years ago
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