4) Find the value of cos(1.74) from the following table H x y = sin(x) 1.7 0.9916 Hint : sin(x) = cos(x) dy dx 1.74 0.9857 1.78 0.9781 1.82 0.9691 1.86 0.9584
4) Find the value of cos(1.74) from the following table H x y = sin(x) 1.7 0.9916 Hint : sin(x) = cos(x) dy dx 1.74 0.9857 1.78 0.9781 1.82 0.9691 1.86 0.9584
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve the question according to my source
Transcribed Image Text:4) Find the value of cos(1.74) from the following table
H
x
y = sin(x)
1.7
0.9916
Hint : sin(x) = cos(x)
dy
dx
1.74
0.9857
1.78
0.9781
1.82
0.9691
1.86
0.9584
Transcribed Image Text:Newton's Forward Differences Formula to get the derivative
We want to find the derivative of y = f(x) passing through the (n+1) points, at a
point nearer to the starting value x = xo.
Newton's Forward Differences Formula
Y(xo+uh) Yo+uAyo + 2!
where u=-
dy 1
dx
dy dy du 1 dy
==
-
dx
du dx h du
A
d²y 1
=
dx² h²
And also
d³y 1
x-xo
h
.
2u-1,
Ayo+ A²y +
2
=
(1/2) - 1/12
=
dx2 du dx dx du dx h
d'y d (dy du d (dy
dx³ h³
24
The above equation gives the value of of general x which may be anywhere in the
interval
E
= 7/34³% +
-
=
u(u-1) u(u-1)(u-2)
-A²yo +
3!
• u du =
dy
dx h
where y= h
A²yo+ (u-1)4³yo +
d²y
=
dx² h²
Y(x)= y(x+yh) = Yn+yVy(n-1) +
x-xn
dy dy dy 1 dy
dx
dy dx hdy
d³y
dx3 3
3u²-6u+2
6
12u - 18
12
Newton's backward differences interpolation formula is :-
y(y + 1) p²y (n)
2!
Newton's Backward Differences Formula to compute the derivative
yn +
2y 1,
1/2 √y₁ + ²y + ¹ v²y₂ + 3y² + 6y + 2
Vyn
2
6
-A*yo +
-1/2 [0²/₁ + (y + 1) 0³ y + 1
12y + 18
12
-4³% +
6u²-18u+11
12
4u³-18u² +22u-6
-4³% +...
6y² + 18y + 11
12
-Vªyn + ...
-Ayo +...
-A¹yo +
4y³ + 18y² + 22y +6,
+-
24
y(y + 1)(y + 2)p³y(n) +-
3!
*y+...
vyn+
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
