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Author Question: Find the maximum value of on [0, 1], where f(x) = e-x2, and use it to obtain an upper bound for the ... (Read 67 times)

tsand2

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Question 1

Let f(x) be a function such that  - 9 ≤  f"(x) ≤ 3, for x∈[2, 4] and let J = dx. Find the maximum absolute error involved in approximating  the integral J using the Trapezoid Rule T10.
◦ 0
◦ 0.06
◦ 0.03
◦ 0.04
◦ 0.02

Question 2

Find the maximum value of    on  [0, 1],  where  f(x) = e-x2, and use it to obtain an upper bound for the absolute value of the error  involved if the Trapezoid Rule approximation based on  n  equal subintervals is used to approximate  I = dx. How large should  n  be chosen to ensure that the error does not exceed  ?
 ≤  1  on  [0, 1],    ≤  ,  n = 8  will do
 ≤  2  on  [0, 1],    ≤  ,  n = 15  will do
 ≤  2  on  [0, 1],    ≤  ,  n = 9  will do
 ≤  2  on  [0, 1],    ≤  ,  n = 10  will do
 ≤  1  on  [0, 1],    ≤  ,  n = 8  will do


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Marked as best answer by tsand2 on May 26, 2021

s.meritte

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tsand2

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Reply 2 on: May 26, 2021
Great answer, keep it coming :)


phuda

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Reply 3 on: Yesterday
Thanks for the timely response, appreciate it

 

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