Explanation Given: a) | M N − ∫ 1 π 4 tan x d x | ≤ 10 − 4 N . b) | E | ≤ 10 − 4 (error) c) Midpoint rule approximation. d) a = 1 and b = π 4 Formula Used: Midpoint rule error given by: | E | ≤ ( b − a ) 3 24 n 2 [ max | f ' ' ( x ) | ] ; a ≤ x ≤ b Calculation: f ( x ) = tan x f ' ( x ) = sec 2 x f ' ' ( x ) = 2 ( sec x ) sec x tan x f ' ' ( x ) = 2 sec 2 x tan x Maximum value of | f ' ' ( x ) | in the interval 1 ≤ x ≤ π 4 is at x = 3 | f ' ' ( x ) | = | 2 sec 2 x tan x | Graph of | 2 sec 2 x tan x | is given as: From graph it is clear that | 2 sec 2 x tan x | is an increasing function between 1 ≤ x ≤ π 4 ∴ Maximum value | f ' ' ( x ) | = | 2 sec 2 x tan x | occur at x = π 4 ∴ | f ' ' ( x ) | = | 2 sec 2 x tan x | | f ' ' ( x ) | = | 2 sec 2 ...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 8, Problem 103CRE

To determine

Value of $N$ $| M_{N} - \int_{1}^{\frac{π}{4}} \tan x d x | \leq 10^{- 4}$ .

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Chapter 8, Problem 102CRE

Chapter 8, Problem 104CRE

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Chapter 8 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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Value of N | M N − ∫ 1 π 4 tan x d x | ≤ 10 − 4 .

Solution Summary: The author explains that the value of n = 28 is given by the following formula: a = 1 and b = 4.

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Value of $N$ $| M_{N} - \int_{1}^{\frac{π}{4}} \tan x d x | \leq 10^{- 4}$ .

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Chapter 8 Solutions

Value of N | M N − ∫ 1 π 4 tan x d x | ≤ 10 − 4 .

Solution Summary: The author explains that the value of n = 28 is given by the following formula: a = 1 and b = 4.

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Value of N|MN−∫1π4tanxdx|≤10−4.

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Chapter 8 Solutions

Value of $N$ $| M_{N} - \int_{1}^{\frac{π}{4}} \tan x d x | \leq 10^{- 4}$ .