Exercise 3. Find f(x) = limn+00 fn(x) on S. Show that (fn)n converges uniformly to f on closed subsets of S. 1 fn(2) = S = {r : x # ±1}. - 1+ x2n

Q: Evaluate the limit and the function.

A: Here we take N tends to infinity for finding the limit function

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A: Given Information:a) ;; .b) ; .To find:The value of  in both the sequence of functions.Concept…

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Q: == 3.14. Prove l'Hôpital's rule in the following form. Suppose f(a) = f'(a) = f(n-1) (a) = 0, g(a) =…

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A: Function limit and continuity

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Q: t if t3 Find a value of A such that the function f(t) is continuous for all t.

A: We have given f(t).  And f(t) is continuous for all t.  It means f(t) must be continuous at t=3

Q: x² – 16 tate why f(x) is continuous on [1, 2]. x² – 9

A: f(x) is continuous on [a,b] if and only if  1. ∀x0∈(a,b)⊆R, limx→x0f(x)=f(x0) 2. limx→a+f(x)=f(a)…

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A: fx=2x2+4x-6x+3; x≠-3-8                 ; x=-3

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A:

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A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.