C=SN/100000, where SN is your student number Given the sine-polynomial; P(x) = −(C/25)x² sin³ x+(−x³ +2 −4x²) sin³ x + (2x-2x-2x4) sin² x+(3x+2x4 −4−x² −4x³) sin x + 2+8x-4x-7x³-x+ (C/27)x² Knowing that this function has three roots in the interval [-1.5, 2.5], to be sure plot the given function over that interval. Find the roots of the above polynomial correct to 100 SFs Using Maple : i. Find the roots using the bisection method (how many iterations needed). ii. Find them using the Newton Raphson method (how many iterations needed). iii. Find them using the secant method (how many iterations needed). iv. Find them using the Newton's second formula (how many iterations needed) which is given as: x+1 = x - f(x) ƒ'(x) = f ( x ) f ( x ) 2f'(x) v. Compare between the results and the methods of parts (i to iv). 2
C=SN/100000, where SN is your student number Given the sine-polynomial; P(x) = −(C/25)x² sin³ x+(−x³ +2 −4x²) sin³ x + (2x-2x-2x4) sin² x+(3x+2x4 −4−x² −4x³) sin x + 2+8x-4x-7x³-x+ (C/27)x² Knowing that this function has three roots in the interval [-1.5, 2.5], to be sure plot the given function over that interval. Find the roots of the above polynomial correct to 100 SFs Using Maple : i. Find the roots using the bisection method (how many iterations needed). ii. Find them using the Newton Raphson method (how many iterations needed). iii. Find them using the secant method (how many iterations needed). iv. Find them using the Newton's second formula (how many iterations needed) which is given as: x+1 = x - f(x) ƒ'(x) = f ( x ) f ( x ) 2f'(x) v. Compare between the results and the methods of parts (i to iv). 2
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SN (student number ) = 0194906
![C=SN/100000, where SN is your student number
Given the sine-polynomial;
P(x) = −(C/25)x² sin³ x+(−x³ +2 −4x²) sin³ x +
(2x-2x-2x4) sin² x+(3x+2x4 −4−x² −4x³) sin x +
2+8x-4x-7x³-x+ (C/27)x²
Knowing that this function has three roots in the interval [-1.5, 2.5], to be sure plot
the given function over that interval. Find the roots of the above polynomial correct
to 100 SFs Using Maple :
i. Find the roots using the bisection method (how many iterations needed).
ii. Find them using the Newton Raphson method (how many iterations needed).
iii. Find them using the secant method (how many iterations needed).
iv. Find them using the Newton's second formula (how many iterations needed)
which is given as:
x+1 = x -
f(x)
ƒ'(x) = f ( x ) f ( x )
2f'(x)
v. Compare between the results and the methods of parts (i to iv).
2](https://content.bartleby.com/qna-images/question/6449428e-0702-4abe-9658-2ec03aee90f4/96a0a3c5-9d10-421f-8d1b-4223c1075300/a3mx2j_processed.jpeg)
Transcribed Image Text:C=SN/100000, where SN is your student number
Given the sine-polynomial;
P(x) = −(C/25)x² sin³ x+(−x³ +2 −4x²) sin³ x +
(2x-2x-2x4) sin² x+(3x+2x4 −4−x² −4x³) sin x +
2+8x-4x-7x³-x+ (C/27)x²
Knowing that this function has three roots in the interval [-1.5, 2.5], to be sure plot
the given function over that interval. Find the roots of the above polynomial correct
to 100 SFs Using Maple :
i. Find the roots using the bisection method (how many iterations needed).
ii. Find them using the Newton Raphson method (how many iterations needed).
iii. Find them using the secant method (how many iterations needed).
iv. Find them using the Newton's second formula (how many iterations needed)
which is given as:
x+1 = x -
f(x)
ƒ'(x) = f ( x ) f ( x )
2f'(x)
v. Compare between the results and the methods of parts (i to iv).
2
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