Find the values of x for which the given geometric series converges. Also, find the sum of the series (as a function of x) for those values of x. ∑ n = 0 ∞ sin n x Find the values of x for which the given geometric series converges. Choose the correct answer below. A. |x| < 1 2 B. x ≠ kπ, k an integer C. x ≠ (2k+1)π 2, k an integer ∑ n = 0 ∞ sin n x = ◻
Use series to approximate the value of the integral with an error of magnitude less than 10 −8. ∫ 0 0.18 sinx x dx ∫ 0 0.18 sinx x dx ≈ ◻ (Round to eight decimal places as needed.)
Use series to approximate the value of the integral with an error of magnitude less than 10 −8 . ∫ 0 0.14 sinx x dx ∫ 0 0.14 sinx x dx ≈ ◻ (Round to eight decimal places as needed.)
Use series to approximate the value of the integral with an error of magnitude less than 10 −8. ∫ 0 0.13 sinx x dx ∫ 0 0.13 sinx x dx ≈ ◻ (Round to eight decimal places as needed.)
Use series to approximate the value of the integral with an error of magnitude less than 10 −8. ∫ 0 0.12 sinx x dx ∫ 0 0.12 sinx x dx ≈ ◻ (Round to eight decimal places as needed.)
Use a series to estimate the following integral's value with an error of magnitude less than 10 −8. ∫ 0 0.3 e −x2 dx ∫ 0 0.3 e −x2 dx ≈ ◻ (Do not round until the final answer. Then round to five decimal places as needed.)
Use series to approximate the value of the integral with an error of magnitude less than 10 −8. ∫ 0 0.22 sinx x dx ∫ 0 0.22 sinx x dx ≈ ◻ (Round to eight decimal places as needed.)
Use series to estimate the integral's value with an error of magnitude less than 10 −3. ∫ 0 0.25 1 1 + x 4 dx ∫ 0 0.25 1 1 + x 4 dx ≈ ◻ (Round to three decimal places as needed.)
Use a Taylor series to approximate the following definite integral. Retain as many terms as needed to ensure the error is less than 10 −4. ∫ 0 0.37 ln(1 + x 2)dx Rewrite the given integral using a Taylor series and simplify the result. Choose the correct answer below. A. ∫ 0 0.37 ( x + x 2 2 + x 3 3 + x 4 4 + … ) d x B. ∫ 0 0.37 ( x + x 2 2 ! + x 3 3 ! + x 4 4 ! + … ) d x C. ∫ 0 0.37 ( x − x 2 2 ! + x 3 3 ! − x 4 4 ! + … ) d x D. ∫ 0 0.37 ( x 2 − x 4 2 + x 6 3 − x 8 4 + … ) d x E. ∫ 0 0.37 ( x 2 + x 4 2 + x 6 3 + x 8 4 + … ) d x F. ∫ 0 0.37 ( x − x 2 2 + x 3 3 − x 4 4 + ⋯ ) d x G. ∫ 0 0.37 ( x 2 − x 4 2 ! + x 6 3 ! − x 8 4 ! + … ) d x H. ∫ 0 0.37 ( x 2 + x 4 2 ! + x 6 3 ! + x 8 4 ! + … ) d x Evaluate the integral such that the error is less than 10 −4. ∫ 0 0.37 ln(1 + x 2) dx = ◻ (Round to four decimal places as needed.)
Use series to approximate the value of the integral with an error of magnitude less than 10 −5. ∫ 0 0.6 1 + x 9 dx ∫ 0 0.6 1 + x 9 dx ≈ ◻ (Round to five decimal places as needed.)