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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
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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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).
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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