ere exists a µ e (a, b) for which the Composite Šimpson' written with its error term as (n/2)-1 n/2 f(x) dx f(a) + 2 f(x2;) +4f (x2j–1) +
ere exists a µ e (a, b) for which the Composite Šimpson' written with its error term as (n/2)-1 n/2 f(x) dx f(a) + 2 f(x2;) +4f (x2j–1) +
Chapter6: Exponential And Logarithmic Functions
Section6.7: Exponential And Logarithmic Models
Problem 27SE: Prove that bx=exln(b) for positive b1 .
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Show that the approximation obtained from Rk,2 is the same as that given by the Composite Simpson’s rule described in Theorem 4.4 with h = hk.
Theorem 4 uploaded for reference
![Let f e C*[a, b], n be even, h = (b – a)/n, and x; = a + jh, for each j = 0,1,...,n.
There exists a u e (a,b) for which the Composite Simpson's rule for n subintervals can
be written with its error term as
(n/2)–1
n/2
h
f(x) dx =
f(a) +2 E fx2;) + 4£f(nj-1) + f (b)
b-a f().
180
j=1
j=l](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13e0b5c3-c232-469d-b8df-18f270097d8e%2F60d469da-1537-4423-b841-68410863f113%2Fvrc746c_processed.png&w=3840&q=75)
Transcribed Image Text:Let f e C*[a, b], n be even, h = (b – a)/n, and x; = a + jh, for each j = 0,1,...,n.
There exists a u e (a,b) for which the Composite Simpson's rule for n subintervals can
be written with its error term as
(n/2)–1
n/2
h
f(x) dx =
f(a) +2 E fx2;) + 4£f(nj-1) + f (b)
b-a f().
180
j=1
j=l
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