
Newton's Method and Its Applications
Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Practice Problem
•
Hard
Thomas White
FREE Resource
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary purpose of Newton's Method?
To find the exact roots of equations.
To approximate the roots of equations.
To graph functions accurately.
To solve linear equations.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In Newton's Method, what is the first step in the iterative process?
Draw the graph of the function.
Find the x-intercept of the tangent line.
Calculate the derivative of the function.
Make an initial guess for the root.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of the tangent line in Newton's Method?
It determines the maximum value of the function.
It is used to approximate the next guess for the root.
It is used to calculate the area under the curve.
It helps in finding the slope of the function.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the next approximation (x2) calculated in Newton's Method?
By adding the function value to the initial guess.
By subtracting the function value from the initial guess.
By subtracting the function value divided by its derivative from the initial guess.
By adding the derivative value to the initial guess.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the general formula for the next approximation in Newton's Method?
Xn+1 = Xn + f(Xn) / f'(Xn)
Xn+1 = Xn / f(Xn) * f'(Xn)
Xn+1 = Xn - f(Xn) / f'(Xn)
Xn+1 = Xn * f(Xn) / f'(Xn)
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example function f(x) = 1/3 x^3 + 1/2 x^2 + 3, what is the derivative f'(x)?
x^2 + x
1/3 x^2 + 1/2 x
3x^2 + 2x
x^2 + 2x
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the approximate value of x2 after the first iteration in the given example?
-3.25
-3.00
-2.75
-2.50
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