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If f has a continuous second derivative on [a, b], then the error E in approximating f(x) dx by the Trapezoidal Rule is (b − a)³ |E| ≤ 12n² Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating [ f(x) dx by Simpson's Rule is (b-a) 180n |Ε| = -[max (4)(x)], a ≤x≤ b. Use these to find the minimum n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using the Trapezoidal Rule and Simpson's Rule. e²x dx n -[max IF"(x)], a ≤ x ≤ b. (a) the Trapezoidal Rule n= (b) Simpson's Rule

If f has a continuous second derivative on [a, b], then the error E in approximating f(x) dx by the Trapezoidal Rule is (b − a)³ |E| ≤ 12n² Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating [ f(x) dx by Simpson's Rule is (b-a) 180n |Ε| = -[max (4)(x)], a ≤x≤ b. Use these to find the minimum n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using the Trapezoidal Rule and Simpson's Rule. e²x dx n -[max IF"(x)], a ≤ x ≤ b. (a) the Trapezoidal Rule n= (b) Simpson's Rule

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 20CR
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If f has a continuous second derivative on [a, b], then the error E in approximating ["(x) f(x) dx by the Trapezoidal Rule is (b − a)³ 12n² |E| ≤ Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating f(x) dx by Simpson's Rule is (b-a) 180n |E| ≤ [max (4)(x)], a ≤x≤ b. Use these to find the minimum n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using the Trapezoidal Rule and Simpson's Rule. n -[max [f"(x)], a ≤ x ≤ b. Le²x dx (a) the Trapezoidal Rule ♫= (b) Simpson's Rule
Transcribed Image Text:If f has a continuous second derivative on [a, b], then the error E in approximating ["(x) f(x) dx by the Trapezoidal Rule is (b − a)³ 12n² |E| ≤ Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating f(x) dx by Simpson's Rule is (b-a) 180n |E| ≤ [max (4)(x)], a ≤x≤ b. Use these to find the minimum n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using the Trapezoidal Rule and Simpson's Rule. n -[max [f"(x)], a ≤ x ≤ b. Le²x dx (a) the Trapezoidal Rule ♫= (b) Simpson's Rule
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