please i need the question 9 and 10 for the detailed proof and explaination ! thanks !
please i need the question 9 and 10 for the detailed proof and explaination ! thanks ! akx*, then for what values does the series 9. If R is the radius of convergence for Σ000 Σ000Akx-k converge? Exp...
Σ (-1)n(7x+6 ,- Consider the series (a) Find the series' radius and interval of convergence (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally? (a) Find the interval of convergence Find the radius of convergence (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally? Select the correct choice below and, if necessary, fill in...
10. Read through the following "e-free" proof of the uniform convergence of power series. Does it depend on limn→oo lan|1/n or lim supn→oo lan! an)1/n? Explain. 1.3 Theorem. For a given power series Σ ak-a)" define the number R, 0 < R < oo, by n-0 lim sup |an| 1/n, then (a) if |z- a < R, the series converges absolutely (b) if lz-a > R, the terms of the series become unbounded and so the (c) if o<r <...
(a) Find the series' radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally Σ (-1)" *'(x+12)" n12" (a) The radius of convergence is (Simplify your answer.) Determine the interval of convergence. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The interval of convergence is (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers...
8n xon Со n=1 (a) Find the series' radius and interval of convergence. (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally? (a) Find the interval of convergence. W Find the radius of convergence. R= (b) For what values of x does the series converge absolutely? X lol Enrnchat online of doon tha nnrin nominoon nanditinnalla calant the norant nhninn holoses and if Click to select your...
k=1 Question 4. Suppose that the power series ax (x – 2)* converges at x = 5 and diverges at x = -7. Write four real numbers at which the series converges and two real numbers at which the series diverges. What can you say about the radius of convergence? Explain your answers clearly.
For what values of x does the series converge absolutely? S (-1)" (2 +9) -1 -10 4 % < -8 -10 E 48 -10 4 0 4 -8 -10 4 8
please i need the question 9 for the detailed proof and explaination ! thanks ! 9. Let 1 fn(ar) 0 1 хи п1+ пx Show that fn0 in C([0,1], R) 9. Let 1 fn(ar) 0 1 хи п1+ пx Show that fn0 in C([0,1], R)
(1 point) For what values of 3 does the series (-1)"n!(1 - 9)" gh 10 M8 converge? The series converges when I is in Use interval notation to enter your answer. If the series converges at only one number, enter a closed interval or a single point, e.g. 15,51" or {5}- Otherwise, enter an open interval (don't worry about whether the series converges at endpoints).
4. [-/10 Points] DETAILS SCALCET8 11.8.AE.002. MY NOTES EXAMPLE 2 For what values of x does the series § (x – 3)" converge? n = 1 SOLUTION Let a, = (x - 3)"/n. Then an + 1 n (x - 3)" 1x - 3 → as n 00. and divergent when x - 3 > Now By the Ratio test, the given series is absolutely convergent, and therefore convergent, when |x - 3|< |x - 3| <1 | <x -...
please i need the question 15 for the detailed proof and explaination ! thanks ! 233 42 Isometries, Conformal Maps 14, we say that a differentiable map ф: S,--S2 preserves angles when for every p e Si and every pair vi, v2 E T (S,) we have cos(u, 2) cos(dp, (vi). do,()). Prove that pis locally conformal if and only if it preserves angles. 15. Letp: R2 R2 be given by ф(x, y)-(u (x, y), u(x, y), where u and...