MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Example Video Example) (a) Approximate the sum of the series by using the fir

[answerhappygod]

My Notes Ask Your Teacher Practice Another Example Video Example A Approximate The Sum Of The Series By Using The Fir 1 (42.62 KiB) Viewed 24 times

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Example Video Example) (a) Approximate the sum of the series by using the first 10 terms. Estimate the error involved in this approximation. (b) How many terms are required to ensure that the sum is accurate to within 0.0005? Solution In both parts (a) and (b) we need to know f(x) dx. With F(x) = which satisfies the conditions of the Integral Test, we have the following. Lºrem I ܂ - 7x dx = lim 1 2x le lim 1 1 8t + - 2nº (a) Approximating the sum of the series by the tenth partial sum, we have the following. 1 = 1 19 10 1 2° + 1 + 39 + (rounded to four decimal places) 9 109 nin According to the remainder estimate in the Remainder Estimate for the Integral Test, we have poo 1 Ros R305 Sam dx = 10 x so the size of the error is at most 0.00000000125. 00 1 (b) Accuracy to within 0.0005 means that we have to find a value of n such that R, S 0.0005. Since RAS - < 0.0005. Solving this inequality, we get dx = we want 1 ns V or n> 250 We need terms to ensure accuracy to within 0.0005.