PLEASE ANSWER ALL BY USING MATLAB ONLY!!!!! (1) Find the relative error of appro

ID: 3110808 • Letter: P

Question

PLEASE ANSWER ALL BY USING MATLAB ONLY!!!!!

(1) Find the relative error of approximation of f(0.2) by the Right End 3-point formula with mesh size h = 0.010, where f(x) = arctan(9x).

(A) 1.3132·104 (B) 8.4710·105 (C) 3.7272·103 (D) 2.3243·103 (E) 2.8627· 103

(2) Find the relative error of approximation of f(1.3) by the Right End 3-point formula with mesh size h = 0.010, where f(x) = arctan(2x).

(A) 8.6938·105 (B) 3.8358·103 (C) 6.0121·104 (D) 1.5151·103 (E) 2.0139· 104

(3) Find the relative error of approximation of f(1.3) by the Left End 5-point formula with mesh size h = 0.005, where f(x) = arctan(8x).

(A) 1.4126·107 (B) 2.6942·109 (C) 2.2190·105 (D) 4.7860·109 (E) 6.1681· 1010

(4) Find the relative error of approximation of f(1.2) by the Left End 5-point formula with mesh size h = 0.005, where f(x) = arctan(8x).

(A) 3.2643 · 106 (B) 6.5092 · 109 (C) 1.9390 · 106 (D)3.0764 108 (E)1.7629.10-9

Solution:

[1]

Answer: (E) 2.8627· 103

Explanation matlab code:

%Right End 3-point formula
y = (atan(9*0.18)-(4*atan(9*0.19))+(3*atan(9*0.2)))/0.02

%direct derivative
x=9/(1+(1.8*1.8))

%relative error
(x-y)/y

Output:

ans = 0.0028709

(2)

answer: (A) 8.6938·105

Code:

%Right End 3-point formula
y = (atan(2*1.28)-(4*atan(2*1.29))+(3*atan(2*1.3)))/0.02

%direct derivative
x=2/(1+(2.6*2.6))

%relative error
(x-y)/y

Outpiut:

%Right End 3-point formula
y = (atan(2*1.28)-(4*atan(2*1.29))+(3*atan(2*1.3)))/0.02

%direct derivative
x=2/(1+(2.6*2.6))

%relative error
(x-y)/y

Hope this Helps!!

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