Let fn (x)= exp (-x^)+1 for all x E Co,1] far allneN*then which is true ?9 (Fn)n Converse s pointwiely to fiCo,!]R where flx)= 22) (Pn)nis increase and lim3) n)n converses uniformly Co,l]4) (Fn)n is decreasing and limlim fnx)deL

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Let fn(x)= exp (-x^)+1 for all xE Lo,1] for allneN* Cer Pn (x)= exp (-x^)+) for all x e [o,l] Por allneN* then which is true ! 9 (Fn)n Converse s pointwiely to fiCo,!]R where flx)= 2 2) (fn )n is inerease and lim fn lx)dHL=2 3) (Fn)n converses unifurmly [o,l] 4) (Fn)n is decreasing and lim fn(w) duL lim fnx)deL

Let fn(x)= exp (-x^)+1 for all xE Lo,1] for allneN* Cer Pn (x)= exp (-x^)+) for all x e [o,l] Por allneN* then which is true ! 9 (Fn)n Converse s pointwiely to fiCo,!]R where flx)= 2 2) (fn )n is inerease and lim fn lx)dHL=2 3) (Fn)n converses unifurmly [o,l] 4) (Fn)n is decreasing and lim fn(w) duL lim fnx)deL

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Let fn (x)= exp (-x^)+1 for all x E Co,1] far allneN*
then which is true ?
9 (Fn)n Converse s pointwiely to fiCo,!]R where flx)= 2
2) (Pn)nis increase and lim
3) n)n converses uniformly Co,l]
4) (Fn)n is decreasing and lim
lim fnx)deL

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