QUESTION 4 You are computing a root of f(x) = cos(x) -x in the interval [0,2] using the bisection method. If you require a result that s accurate to within five significant digits, which of the following bounds holds for the minimum number of bisection iterations k required? O 1/2-1<10-5 O 1/2 <10-5 O 2/2+1 <10-5 O None of the above QUESTION 5 The irrational number √2 can be approximated by applying the secant method to the nonlinear equation x²-2=0. What is the iteration formula? O x²-2 O H (x2-2)(x-x-1) x₂ + x₁-1
QUESTION 4 You are computing a root of f(x) = cos(x) -x in the interval [0,2] using the bisection method. If you require a result that s accurate to within five significant digits, which of the following bounds holds for the minimum number of bisection iterations k required? O 1/2-1<10-5 O 1/2 <10-5 O 2/2+1 <10-5 O None of the above QUESTION 5 The irrational number √2 can be approximated by applying the secant method to the nonlinear equation x²-2=0. What is the iteration formula? O x²-2 O H (x2-2)(x-x-1) x₂ + x₁-1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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![QUESTION 4
You are computing a root of f(x) = cos(x) -x in the interval [0, 2] using the bisection method. If you require a result that is accurate to within five significant digits, which of the following bounds holds for the
minimum number of bisection iterations k required?
O
1/2k-¹ <10-5
1/2k <10-5
2/2+¹ <10-5
+1
None of the above
QUESTION 5
The irrational number √2 can be approximated by applying the secant method to the nonlinear equation x²-2=0. What is the iteration formula?
x²-2
k
X
k+1 k
X
=X -
=X
k+1 k
x
=X
k + 1 k
X
k+1
=X
k
x + x
k
k-1
(x²-2) (x₂-x-₁)
k
k-1
x + x
k
k-1
(x²-2)(x-x-₁)
k
x²+x²2_1
k
k-1
(x²-2)(x-x-1)
x²-x²_₁-
k k-1
- 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01b4eff1-1c92-4d86-9563-264f29556131%2F3e02891f-03e1-4fdf-a0a3-463554eb7370%2Fndx7ib_processed.jpeg&w=3840&q=75)
Transcribed Image Text:QUESTION 4
You are computing a root of f(x) = cos(x) -x in the interval [0, 2] using the bisection method. If you require a result that is accurate to within five significant digits, which of the following bounds holds for the
minimum number of bisection iterations k required?
O
1/2k-¹ <10-5
1/2k <10-5
2/2+¹ <10-5
+1
None of the above
QUESTION 5
The irrational number √2 can be approximated by applying the secant method to the nonlinear equation x²-2=0. What is the iteration formula?
x²-2
k
X
k+1 k
X
=X -
=X
k+1 k
x
=X
k + 1 k
X
k+1
=X
k
x + x
k
k-1
(x²-2) (x₂-x-₁)
k
k-1
x + x
k
k-1
(x²-2)(x-x-₁)
k
x²+x²2_1
k
k-1
(x²-2)(x-x-1)
x²-x²_₁-
k k-1
- 4
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