Let g be a differentiable function with g(-1)=5 and g'(-1)=2. What is the value of the approximation of g(-0.9) using the function's local linear approximation at x= -1?

Options: 5.1, 5.2, 5.3, or 5.4​

Answers

Answer 1

Answer:

5.2

Step-by-step explanation:

g(x) = mx +b

g'(x) = m = 2 for all x

g(-1) = 2(-1) + b = 5

-2 + b = 5

b = 7

So, g(x) = 2x + 7

Therefore g(-.9) = 2(-.9) + 7

= -1.8 + 7 = 5.2

Answer 2

The value of g(-0.9) is equal to 5.2.

What is a Function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

As per the given data:

g(x) is a differentiable function.

We have to use the function's local linear approximation at x = -1.

g(-1) = 5

g'(-1) = 2

As We have to use the function's local linear approximation:

Let assume, g(x) = mx + b

Differentiating both sides,

g'(x) = m

∴ g'(-1) = 2 = m

m = 2

g(x) = 2x + b ...(i)

g(-1) = 5

Using in eq (i)

5 = -2 + b

b = 7

g(x) = 2x + 7

Let's substitute x = -0.9 to find out the answer.

g(-0.9) = 2(-0.9) + 7

= 7 - 1.8 = 5.2

The value of g(-0.9) is equal to 5.2.

Hence, The value of g(-0.9) is equal to 5.2.

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Answers

Answer:

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Step-by-step explanation:

Let us solve the question

∵ The rule is On = Q1 + (n - 1)d

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

[tex] \sqrt[4]{256} [/tex]

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Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answer:

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----------------------------------------------------------------------------------------------------

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(0,1)

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-------------------------------------------

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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The drawing below (not to scale) shows a running track. The ends are semicircles. The distance between the two inner parallel straight lines is 60 meters, and they are each 100 meters long. The track is 10 meters wide/

Answers

Answer:

4200 m²

Step-by-step explanation:

The drawing below (not to scale) shows a running track. The ends are semicircles. The distance between the two inner parallel straight lines is 60 meters, and they are each 100 meters long. The track is 10 meters wide. Find the area of the track. Shaded part

Solution:

The big semicircle has a diameter = 60 m + 10 m + 10 m = 80 m

The radius of the big semicircle = 80 m / 2 = 40 m

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Answers

Answer:

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Step-by-step explanation:

The area of the shaded region is calculated as

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area of inner = [tex]\frac{1}{2}[/tex] × 12 × 5 = 30 cm²

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Answers

Answer:

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Step-by-step explanation:

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