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- Represent the function 5x 00 as a power series f(x) = >, 6+ x Cnx" n=0 1 = 2 = 3 = 4=st Find the 1 three terms in Taylor series for f(x) = sinTX near x-0.5.Evaluate the infinite series by identifying it as the value of a derivative of a geometric series. ∞∑n=1 of n/6^n Hint: Relate it to f'(1/6) where f(x)=∞∑n=0 of x^n
- Find a power series for f(x) = 5/(3-x) centered at 0.Evaluate the infinite series by identifying it as the value of a derivative of a geometric series. n(n − 1) 3n ∞ n=2 = (²) 3 Hint: Write it as f'' where f(x) = £². n=0< =] Q2. Find the Fourier series for the function f(x) = x- x² for – nLet f(x)=e(x-1)^2-1/(x-1)2 for x ≠ 1 and f(1)=1 d. Use the series for f about x=1 to determine if the graph of f has any points of inflection.13.) Find a power series for the function f(x) = = 5 2-6x3*Evaluate the infinite series by identifying it as the value of a derivative of a geometric series. п 5" n=1 (5) Hint: Write it as f' where f(x) = n=0 Question Help: Message instructor Submit Question Jump to AnswerSEE MORE QUESTIONS
