Question 4. Let f be the function defined by the series f(z) = E for all z such that -1 < z < 1. Which statements do hold? a) The series converges absolutely. b) The derivative is f'(2) = [=". c) The derivative is s'(x) = £=". d) The derivative equals f'(z) :

Q: Which of the following information is correct for the sequence 3 7 dx 1 dx 1 dx dx {an}n=l X (a) The…

A: Given: The given sequence is ann=1∞=13∫13dxx,15∫15dxx,17∫17dxx,19∫19dxx.....

Q: cosh(2.r) - 1 6. (a) Show that sinh (r) %3D 2

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: How would I find if the sequences an=nπ cos(nπ) and an= (n2)(1/n) are convergent/divergent?

A: To examine the given sequence regarding convergence, that is study the limits as n tends to infinity

Q: #3. Prove that 2 = tan [ = log (T_-_ iz)

A: To Prove:z=tan1ilog1+iz1-iz12.

Q: If the series En=1 an converges absolutely, the sequence {b,} is bounded, then the series sin(a,)b,…

A: ∑ann=1∞ is absolutely convergent and bn is bounded .

Q: (e) Č(-1)"e Σ (-1)"e¯n

A:

Q: Let a„(x) = (n + 1)²™”, and define f(x) = an(x). n=0 a) Evaluate the following quantities: lim h(x)…

A: We have;

Q: 3. Find the interval of convergence of the series ☎ n=1 (-1)"+¹(x-2)" 3"-n

A: Find the interval of convergence of the series

Q: z-i) in the following (6) 1 <시리 <2 (C) r

A:

Q: Define Find the values of x where the series converges and show that we get a continuous function on…

A: The given series is g(x)=∑n=0∞x2n1+x2n. To Find: The values of x for which the series is convergent.…

Q: Theorem 17 (H.w) If lim x, # 0 then E=1Xn diverges series.

A:

Q: (b) (a) -5 Q7) L(y") = a) s²L(y(x)) + sy(0) - y'(0) c) s²L(y(x))-sy(0) - y'(0) b) s² L(y(x)) + sy(0)…

A: We have to find the correct choice.

Q: Find the common ratio for the geometric series + (1-) + (1- 2)* + (1- )° +… ,and hence find the…

A: Solution is given below..

Q: A10. If f(x)=1- -+-----is an infinite series, then which of the following is t 1! 2! 3! 4! 5! a)…

A:

Q: ttempt to use the Root Test to decide whether the series converges. L = lim lan| n00 of the limit L…

A: In this question, the concept of convergence is applied. Convergence The feature of approaching a…

Q: Question 4. Let f be the function defined by the series f(r) = for all z such that -1 < r < 1. Which…

A:

Q: 6. If f(x) = then the Maclaurine series for f(x) is ++3x a) c) Ž3x) b) E-D* 3* x* d) Ž(-1)" x*

A:

Q: Let f be the function defined by the series f(r) = E for all r such that -1 < x < 1. Which 72…

A: Consider the function fx=∑n=1∞xnn, for all x such that -1&lt;x&lt;1. (a) To check whether the series…

Q: 24. Let f be a function such that f'(x) Maclaurin series for f? = sin 9 (A) x - + 10 216 9 X (B) 2x…

A: Step 1:Step 2:

Q: Σ Suppose that ax" converges to a function y such that y" – 2y' + y = 0 where y(0) = 0 and y'(0) =…

A:

Q: 6. Let f(x)=L - 2x, 0 < x < L. (a) Find the cos series for f(x) with period 2L. (b) Sketch the graph…

A: