Let f be the function defined by the rule f(x)=√√ on the interval (81, 84). Since f is known to be continuous and differentiable on this domain, the mean value theorem says that f(84)-(81) 84-81 (an expression in c),
Let f be the function defined by the rule f(x)=√√ on the interval (81, 84). Since f is known to be continuous and differentiable on this domain, the mean value theorem says that f(84)-(81) 84-81 (an expression in c),
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![The mean value theorem can also be used to find bounds for errors in approximations. Consider the following
examples.
Note: Remember to write your answers using Matlab syntax.
For example,
2+1
would be written as
2-2c
b^(1/3) *sqrt((x+1)/(x^2-2*c))
Let f be the function defined by the rule
f(x)=√√
on the interval [81, 84]. Since f is known to be continuous and differentiable on this domain, the mean value theorem
says that
f(84)-f(81)
84-81
for some c E (81, 84).
Hence, we can conclude that
for some 0<<
√√84-9+8.
(an expression in c),
Alternatively, let g be the function defined by
9(2)=¾½
on the interval [64, 67). Since g is known to be continuous and differentiable on this domain, the mean value theorem
says that
for some c (64,67).
Hence, we have that
for some 0 <EA
9(67)-9(64)
67-64
3/67=4+.
(an expression in c).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6cd132a-964f-4a31-af3d-1b1c2cf60729%2Fee40f34c-5233-4dc3-9bbf-51ba8f377775%2F72mhnbc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The mean value theorem can also be used to find bounds for errors in approximations. Consider the following
examples.
Note: Remember to write your answers using Matlab syntax.
For example,
2+1
would be written as
2-2c
b^(1/3) *sqrt((x+1)/(x^2-2*c))
Let f be the function defined by the rule
f(x)=√√
on the interval [81, 84]. Since f is known to be continuous and differentiable on this domain, the mean value theorem
says that
f(84)-f(81)
84-81
for some c E (81, 84).
Hence, we can conclude that
for some 0<<
√√84-9+8.
(an expression in c),
Alternatively, let g be the function defined by
9(2)=¾½
on the interval [64, 67). Since g is known to be continuous and differentiable on this domain, the mean value theorem
says that
for some c (64,67).
Hence, we have that
for some 0 <EA
9(67)-9(64)
67-64
3/67=4+.
(an expression in c).
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