1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Irina18 [472]
3 years ago
14

Calculate two iterations of Newton's Method for the function using the given initial guess. (Round your answers to four decimal

places.) f(x) = x2 − 8, x1 = 2
Mathematics
1 answer:
pickupchik [31]3 years ago
7 0

Answer:

The first and second iteration of Newton's Method are 3 and \frac{11}{6}.

Step-by-step explanation:

The Newton's Method is a multi-step numerical method for continuous diffentiable function of the form f(x) = 0 based on the following formula:

x_{i+1} = x_{i} -\frac{f(x_{i})}{f'(x_{i})}

Where:

x_{i} - i-th Approximation, dimensionless.

x_{i+1} - (i+1)-th Approximation, dimensionless.

f(x_{i}) - Function evaluated at i-th Approximation, dimensionless.

f'(x_{i}) - First derivative evaluated at (i+1)-th Approximation, dimensionless.

Let be f(x) = x^{2}-8 and f'(x) = 2\cdot x, the resultant expression is:

x_{i+1} = x_{i} -\frac{x_{i}^{2}-8}{2\cdot x_{i}}

First iteration: (x_{1} = 2)

x_{2} = 2-\frac{2^{2}-8}{2\cdot (2)}

x_{2} = 2 + \frac{4}{4}

x_{2} = 3

Second iteration: (x_{2} = 3)

x_{3} = 3-\frac{3^{2}-8}{2\cdot (3)}

x_{3} = 2 - \frac{1}{6}

x_{3} = \frac{11}{6}

You might be interested in
Please help me out with this
adoni [48]
The numbers in the chart are -7.1, -3.4, -1.2, 2.1, and 3.4. So, from greatest to least the numbers will be:

3.4, 2.1, -1.2, -3.4, and then -7.1.

With absolute value, the numbers from greatest to least are: 

|7.1|, |3.4|, 3.4, 2.1, |1.2|.

However, this is assuming that Friday is 3.4, which was given information on the last question. Hope this helps!
4 0
3 years ago
Paul predicts that n stalks of corn planted together will produce (2n2–2n)(2n2–2n) ears of corn. If Paul plants three corn plant
Free_Kalibri [48]
Given that the production of n stalks of corn planted has been modeled by (2n^2-2n), then the approximate ears of corn produced by 3 stalks will be given by:
2n^2-2n
plugging in n=3 in the formula we get:
2(3)^2-2(3)
simplifying we get:
2(9)-6
=18-6
=12
the answer is: 12 ears
6 0
3 years ago
Yesterday, Grace drove 2 1/8 miles. she used 1 1/4
prisoha [69]

Answer:

7/8

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Fanning + medal
lubasha [3.4K]
The Greatest Common Factor of the given expression should be that expression that can divide both. First, factor both expression,
           x^4 = (x³)(x)      and x³ = (x³)(1)
Therefore, both can be factored by x³. The answer is the third choice. 
7 0
2 years ago
Read 2 more answers
If the height of the box is 7 inches, the volume of the box will be [1] cubic inches.
Rainbow [258]

Answer:

I dont really get it-

Step-by-step explanation:

whats the question?

6 0
2 years ago
Read 2 more answers
Other questions:
  • Canned dog food is on sale fo 20% off the original price. What is the discount of a can if the original price is $1.35
    6·2 answers
  • How do you write 77/200 as a decimal
    14·2 answers
  • Help me ! please thamks
    15·1 answer
  • Simplify the expression (-4)(9)/(-6)<br><br>6<br><br>–36<br><br>36<br><br>–6
    15·1 answer
  • To estimate your average monthly salary, divide your salary by the number of months in a year. Write and solve an equation to de
    6·1 answer
  • Select ALL the measures of volume.
    8·1 answer
  • Problem #3
    6·1 answer
  • I need help I need this plz
    13·1 answer
  • Ratio..A candy store sells snacks by weight. A six ounce bag of candy cost $3.60. Predict the cost of a 2ounce bag.
    5·1 answer
  • PLEASE HELP 30 cm
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!