![real analysis - prove function series $f_n(x)=(\sin x)^{1/n} $ doesn' converge uniformly - Mathematics Stack Exchange real analysis - prove function series $f_n(x)=(\sin x)^{1/n} $ doesn' converge uniformly - Mathematics Stack Exchange](https://i.stack.imgur.com/LVqX2.jpg)
real analysis - prove function series $f_n(x)=(\sin x)^{1/n} $ doesn' converge uniformly - Mathematics Stack Exchange
Real Analysis II Chapter 9 Sequences and Series of Functions 9.1 Pointwise Convergence of Sequence of Functions Definition 9.1 A
Which of the following sequences of functions is uniformly convergent on (0, 1)?a)1/(nx + 1)b)xnc)n/(nx + 1)d)x/(nx + 1)Correct answer is option 'D'. Can you explain this answer? | EduRev Mathematics Question
![SOLVED: EXAMPLE 1 CnzL Here the ratio test gives A2di 1m;vnna n? @n+l xn+l n2 (- 46 lim lim lim Ix| = Ixl: n+00 @n n-00 (n +1)2 n-00 (n + 1)2 " SOLVED: EXAMPLE 1 CnzL Here the ratio test gives A2di 1m;vnna n? @n+l xn+l n2 (- 46 lim lim lim Ix| = Ixl: n+00 @n n-00 (n +1)2 n-00 (n + 1)2 "](https://cdn.numerade.com/ask_images/3b1bdbe9ca7748a18dd7154a195f91d7.jpg)
SOLVED: EXAMPLE 1 CnzL Here the ratio test gives A2di 1m;vnna n? @n+l xn+l n2 (- 46 lim lim lim Ix| = Ixl: n+00 @n n-00 (n +1)2 n-00 (n + 1)2 "
![SOLVED: For problems 2-8 find the pointwise limit of the sequence and determine the interval(s) on which the sequence converges uniformly 2 fn(x) = "x on [0,1] 3 fn (x) = 1+nx SOLVED: For problems 2-8 find the pointwise limit of the sequence and determine the interval(s) on which the sequence converges uniformly 2 fn(x) = "x on [0,1] 3 fn (x) = 1+nx](https://cdn.numerade.com/ask_images/fc3c17a286d2424d883bafddb955f911.jpg)
SOLVED: For problems 2-8 find the pointwise limit of the sequence and determine the interval(s) on which the sequence converges uniformly 2 fn(x) = "x on [0,1] 3 fn (x) = 1+nx
Is the sequence of functions [math] f_n(x) =\frac{nx}{1+(nx)^2)} [/math] uniformly convergent (real calculus, uniform convergence, sequence)? - Quora
![SOLVED: Question Discuss the pointwise convergence and the uniform convergence of the following sequences; 1. fn(z) = 1 sing " 1 € (0,0). 2. fn(x) = e-nrl sin(nx) , I € R SOLVED: Question Discuss the pointwise convergence and the uniform convergence of the following sequences; 1. fn(z) = 1 sing " 1 € (0,0). 2. fn(x) = e-nrl sin(nx) , I € R](https://cdn.numerade.com/ask_images/c47227060a7d461a9892b85e9ca6470c.jpg)