Concept explainers
(a)
The trapezoidal rule approximation for n=10, 100, 1000.
(a)
Answer to Problem 27E
The value of the
Explanation of Solution
Given information:
Consider the integral
Formula used:
Calculation:
In the trapezoidal rule, if [a, b] is partitioned into n subintervals of equal length
The region between the curve and the x-axis is then approximated by the trapezoids, the area of each trapezoid being the length of its horizontal “altitude" times the average of two vertical “bases". That is,
Where,
To find integral use your calculator program of Trapezoidal rule approximations with
Conclusion:
The value of the integral is 1.98, 1.99.
(b)
The decimal places based on recording the errors.
(b)
Answer to Problem 27E
The value of error is
Explanation of Solution
Given information:
Consider the integral
Formula used:
Calculation:
If T represents the approximation to
The error is determined as below,
Where Tn represents the value of integral by trapezoidal rule for different value of n
Conclusion:
The value of error is
(c)
The number of patterns.
(c)
Answer to Problem 27E
The value is
Explanation of Solution
Given information:
Consider the integral
Formula used:
Multiplication is used.
Calculation:
Observe the last column or above table, error gets multiplied approximately each time by 10-2
So,
Conclusion:
The value is
(d)
The error bound for ET accounts for the pattern.
(d)
Answer to Problem 27E
The error bound that accounts for the pattern is
Explanation of Solution
Given information:
Consider the integral
Formula used:
Calculation:
Now, use the formula for error bound
Now,
So,
Hence, error bound accounts for the pattern.
Conclusion:
The error bound that accounts for the pattern is
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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