* Recall that the error due to linear interpolation of the function f(x) on [xo, x1] is f"(Em) e1(2) = f(x) – p1 (2) = (x – ro) (x – 11) 2! for some E E (xo, x1). Suppose that the function f(x) = sin x is tabulated at equal intervals of length h. What value of h will ensure that the use of linear interpolation between two successive entries in this table will produce an error of no more than 0.5 x 10-4?
* Recall that the error due to linear interpolation of the function f(x) on [xo, x1] is f"(Em) e1(2) = f(x) – p1 (2) = (x – ro) (x – 11) 2! for some E E (xo, x1). Suppose that the function f(x) = sin x is tabulated at equal intervals of length h. What value of h will ensure that the use of linear interpolation between two successive entries in this table will produce an error of no more than 0.5 x 10-4?
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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![4. * Recall that the error due to linear interpolation of the function f(x) on [xo, x1] is
f"(§a)
e1(x) = f(x) – P1 (x) = (x – x0) (x – x1)
2!
for some f E (xo, x1).
Suppose that the function f(x) = sin x is tabulated at equal intervals of length h.
What value of h will ensure that the use of linear interpolation between two successive entries in this
table will produce an error of no more than 0.5 x 10-4?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c3ce0fd-4090-405c-80f4-99d74f0446d4%2F66724648-6641-4cf6-8157-77c71f52d3a7%2Fmktb7m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. * Recall that the error due to linear interpolation of the function f(x) on [xo, x1] is
f"(§a)
e1(x) = f(x) – P1 (x) = (x – x0) (x – x1)
2!
for some f E (xo, x1).
Suppose that the function f(x) = sin x is tabulated at equal intervals of length h.
What value of h will ensure that the use of linear interpolation between two successive entries in this
table will produce an error of no more than 0.5 x 10-4?
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