4.20.12515A clamped cubic spline S for a finction f is defined bya(x - 3) + (x-3)²+b(x – 3)*1-2(x 4)-5(x – 4)? + (x - 4)*S(x) =3Sx544Sx55Find a and b if f'(3) = f'(5).a = 2, b = -2.a = -880, b = -174a = 6, b = -2,O a =1, b = 2Let P(x) be the Lagrange interpolating polynomial off(x) =3x2 + 33. If P(x) is used to approximateat the points xo = 0; x1 = 1 and x2 =approximation of f'(2) is most nearly:-0.076-0.100-0.083-0.0667

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A clamped cubic spline S for a finction fis defined by a(x - 3) + (x-3)²+b(x – 3)³ - 2(x-4)-5(x - 4)2 +(x- 4) 45x55 3 SxS4 S(x) = }, %3D Find a and b if f'(3) = f'(5). O a = 2, b = -2. O a =-880, b = -174 O a = 6, b = -2, a =1, b = 2

A clamped cubic spline S for a finction fis defined by a(x - 3) + (x-3)²+b(x – 3)³ - 2(x-4)-5(x - 4)2 +(x- 4) 45x55 3 SxS4 S(x) = }, %3D Find a and b if f'(3) = f'(5). O a = 2, b = -2. O a =-880, b = -174 O a = 6, b = -2, a =1, b = 2

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

4.
20.125
15
A clamped cubic spline S for a finction f is defined by
a(x - 3) + (x-3)²+b(x – 3)*
1-2(x 4)-5(x – 4)? + (x - 4)*
S(x) =
3Sx54
4Sx55
Find a and b if f'(3) = f'(5).
a = 2, b = -2.
a = -880, b = -174
a = 6, b = -2,
O a =1, b = 2
Let P(x) be the Lagrange interpolating polynomial of
f(x) =
3x2 + 3
3. If P(x) is used to approximate
at the points xo = 0; x1 = 1 and x2 =
approximation of f'(2) is most nearly:
-0.076
-0.100
-0.083
-0.0667

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