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Chapter 8 Solutions
Calculus: Early Transcendentals (2nd Edition)
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- 49arrow_forwardx7 1 Given that x" with convergence in (-1, 1), find the power series for with center 1- x 1+ 6x7 n=0 0. 00 n=0 Identify its interval of convergence. The series is convergent from x = , left end included (enter Y or N): to x = , right end included (enter Y or N): Submit Questionarrow_forwardboth otherwise notarrow_forward
- Consider the power series: The interval of convergence goes from x = The radius of convergence is R = If needed, enter INF for ao and -INF for -∞. to x = n=1 (x - 3)" (-10)arrow_forwardInn Use the integral test to find values of p for which the series is convergent: In x why the real valued function ƒ(x)=- -satisfies the hypothesis of the integral test. In particular you need to sow that f'is decreasing eventually on (0,00). Note: State and showarrow_forwardFind Interval of convergencearrow_forward
- 8arrow_forwardΣ x" for x < 1 to expand the function n=0 (Express numbers in exact form. Use symbolic notation and fractions where needed.) Use the equation 2 1 x4 || x E = M8 n=0 1 1 X = 2 1 x4 in a power series with center c = 0. Determine the interval of convergence. (Give your answer as an interval in the form (*,*). Use the symbol ∞ for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)arrow_forwardJause the series ER=1(41)kt1) = (-1)k+1xk determine the Maclaurin series and the interval of convergence for the function f(x) = ln (1-5x²). Write out the series using summation notation and write it out as a sum of at least the first 4 terms (with ellipsis). b) Use the series for f(x) = ln (1-5 x²) that you found in part (a) to evaluate the limit: limx-0 = In (1+x), for-1 < x≤ 1 to 5x²+In(1-5x2) 3x4arrow_forward
- 2" n! Consider the series Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it 5. 8. 11 · · (3n + 2) ... .. n=1 does not exist, type "DNE". an+1 lim = L An Answer: L = What can you say about the series using the Ratio Test? Answer "Convergent", "Divergent", or "Inconclusive".arrow_forwardFind all possible value of x for convergence and divergence botharrow_forwardQuestion = Find the interval of convergence for the power series representing ƒ' if f(x) = interval notation. Provide your answer below: Interval of convergence: 8 −7+x6 .Enter an exact answer inarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage