4. The series f(x) = ² - can be shown to converge on the interval [-1, 1). n=1 n (a) Find the series f'(x) in series form and find its interval of convergence, showing all work and reasoning, of course! (b) Find the series [ f(x) dx in series form and find its interval of convergence, showing all work, of course!
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- The series 0 Cn (x+4)" converges for x = n=0 answer: (i) (ii) (ii) and diverges for x = 3. Circle/indicate the correct Zn=0 0 Cn(-8)" is: (a) convergent; (b) divergent; (c) not enough information. 0 Cn(-7)" is: (a) convergent; (b) divergent; (c) not enough information. Cn4" is: (a) convergent; (b) divergent; (c) not enough information.4. The series f(x) = can be shown to converge on the interval [-1, 1). n=1 n (a) Find the series f'(x) in series form and find its interval of convergence, showing all work, of course! (b) Find the series [ f(x)dx in series form and find its interval of convergence, showing all work, of course!The function f is defined by the power series x7 X f(x) = X 3 5 7 for all real number X for which the series converges. (a) Find the interval of convergence of the power series for f Justify your answer. (b) Write the first four nonzero terms and the general term for an infinite series that represents f'(x) + + (-1)"x2n+1 2n + 1
- Find the interval of convergence of the series. (x+10)'"¹ n8" Ž(-1)". n=1 (-14,2] [−1,1] (-14, -2) (-10,10] (-18, -2) [-10,10] [-18,-2) (-4,14] (-18, -2]The interval of convergent for the series (-1)*x* is: 4kk (a)[-4,4] (b)(-4,4] (c) [-4,4) (d)(-4,4) (e) None a O b C esot agovno Find all numbers x for which the power series (A) 3'3 converges. 3k k=0 1912 (B) [-1, 1] (C) (-3, 3) (D) [-3,3]
- Geometric series can be found by transforming f(x)= to series form using 1-x Maclaurin's series to get = = Lox" = 1 + x + x2 + x3 + x+ + ...... 1) Why this series diverges at x = 4 while the function is defined. 2) Why this series diverges at x = -4 while the function is defined. i need clear ans by hand and solve very very fast in 20 min and thank you | DYBALA =(f(x نص الصورة المكتوب: يمكن إيجاد المتسلسلة الهندسية بتحويل En=0x" =1+x+x2 + x3 + x2 + 1 1-X %] = إلى شكل متسلسلة باستخدام 4 = x متسلسلة ماكلورين للحصول على 1) لماذا هذا تتباعد المتسلسلة عند أثناء تعريف 4- = x أثناء تعريف الدالة. 2) لماذا تتباعد هذه المتسلسلة عند الدالة. أحتاج إلى إجابة واضحة يدويا وحل سريع جدا في 20 دقيقة وشكرا لك | ديبالا =Use the power series 1 1 + x ∞ Σ (-1)^x^, |x| < 1 n = 0 to find a power series for the function, centered at 0. In(x6 + 1) f(x) ∞ = = f(x) = |(−1)¹x6n n = 0 X Determine the interval of convergence. (Enter your answer using interval notation.) (−1,1) XS (x+7)" convergent range of series n=1 Select one: a. (-1-7,1-7] (+-1,1-7) O * [T-1,1-7] O d. [-1-7,1-7) е. * (7-11-7]
- Problem - 1 : Find the interval of convergence of the series -3). 2 (x-3)+.··.+ (x-3)"(-1)*+1gk+2 x' (a) Find a function represented by the power series > k! k=0 (-1)*+1 . 2k+2 3k+2. k! (b) Evaluate the series k=0Q5/ For the following series :- 1 (x-2), (x - 2)2 (x- 2)" f(x). + (-1)". - 4 8 2n+1 Find :- a- Values of (x) that make series converged b- The sum of series Ans./ a) 0SEE MORE QUESTIONS