Suppose you know that
and the Taylor series of ƒ centered at 4 converges to
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- The Taylor series at x = 0 for f(x) = sec x is 1 + £r² + ☆x* + 6+ · … . Find f((0).arrow_forwardLet f(x)=e(x-1)^2-1/(x-1)2 for x ≠ 1 and f(1)=1 a. Write the first four nonzero terms and the general term of the Taylor series for e(x-1)^2 about x=1 b. Use the series found in (a) to write the first four nonzero terms and the general term for the Taylor series for f about x=1 c. Determine the interval of convergence for the series given in (b). d. Use the series for f about x=1 to determine if the graph of f has any points of inflection.arrow_forwarda. Find the Taylor series at 0 by performing operations on the basic Taylor series. State the interval of convergence. f(x)=ln(1+16x^2) Type the first four terms and the nth-term of the Taylor series. f(x)= b.Find the Taylor series at 0 by performing operations on the basic Taylor series. State the interval of convergence. f(x)=4/5+x^2 Type the first four terms and the nth-term of the Taylor series. f(x)= c. Evaluating the Taylor series at 0 for f(x)=e^−x at x=0.8 produces the following series. e^−0.8=1−0.8+0.32−0.085333+0.017067−0.002731+⋯ Use two terms in this series to approximate e^−0.8, and then estimate the error in this approximation. e^−0.8=arrow_forward
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