3. Let f(x) = e²" (a) Find a Trapezoid Rule approximation to *dr using n = 50 subintervals. (Note: For so many calculations you will need to use a computer or calculator. (b) Calculate f"(x) (c) Explain why |f" (x)| < 18 on [0, 1), given that e < 3. (d) Use the formula to find an upper bound on the absolute error in the estimate found in part (a). Here M is an upper bound for the absolute value of f"(x) on the interval from a to b. M(b – a) (Ax)² Er S 12
3. Let f(x) = e²" (a) Find a Trapezoid Rule approximation to *dr using n = 50 subintervals. (Note: For so many calculations you will need to use a computer or calculator. (b) Calculate f"(x) (c) Explain why |f" (x)| < 18 on [0, 1), given that e < 3. (d) Use the formula to find an upper bound on the absolute error in the estimate found in part (a). Here M is an upper bound for the absolute value of f"(x) on the interval from a to b. M(b – a) (Ax)² Er S 12
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![3. Let f(x) = e
(a) Find a Trapezoid Rule approximation to / e dx using n = 50 subintervals. (Note: For so many
calculations you will need to use a computer or calculator.
(b) Calculate f" (x)
(c) Explain why \f" (x)| < 18 on [0, 1], given that e < 3.
(d) Use the formula to find an upper bound on the absolute error in the estimate found in part (a). Here
M is an upper bound for the absolute value of f"(x) on the interval from a to b.
M(b- a) (Ar)?
ET <
12](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadf6522a-836e-432f-b2da-01517f4c2c07%2Fc321cb96-2b81-43d6-8f3d-1cceaca4a3b1%2F3g5ph6_processed.png&w=3840&q=75)
Transcribed Image Text:3. Let f(x) = e
(a) Find a Trapezoid Rule approximation to / e dx using n = 50 subintervals. (Note: For so many
calculations you will need to use a computer or calculator.
(b) Calculate f" (x)
(c) Explain why \f" (x)| < 18 on [0, 1], given that e < 3.
(d) Use the formula to find an upper bound on the absolute error in the estimate found in part (a). Here
M is an upper bound for the absolute value of f"(x) on the interval from a to b.
M(b- a) (Ar)?
ET <
12
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