Do 1 2 and 4th parts 2. Define f(x) =for j=1,2,3..... with domain S – R.1+jr(a) Find f(x) = lim f(x), the pointwise limit of this sequence of functions.(b) Does the sequence of functions {f} converge to f uniformly [0, +00)? Justify.(c) Does the sequence of functions {f} converge to f uniformly (0, +∞o)? Justify.(d) Does the sequence of functions {f} converge to f uniformly [1, +∞)? Justify.

Answered: Image /qna-images/answer/6a33e2dd-55c0-4417-864b-4b3cafc0cbc1.jpg

2. Define f(x) = for j=1,2,3,.... with domain S = R. 1+jr (a) Find f(x) = lim f(x), the pointwise limit of this sequence of functions. (b) Does the sequence of functions {f} converge to f uniformly [0, +∞o)? Justify. (c) Does the sequence of functions {f} converge to f uniformly (0, +∞o)? Justify. (d) Does the sequence of functions {f} converge to f uniformly [1, +∞)? Justify.

2. Define f(x) = for j=1,2,3,.... with domain S = R. 1+jr (a) Find f(x) = lim f(x), the pointwise limit of this sequence of functions. (b) Does the sequence of functions {f} converge to f uniformly [0, +∞o)? Justify. (c) Does the sequence of functions {f} converge to f uniformly (0, +∞o)? Justify. (d) Does the sequence of functions {f} converge to f uniformly [1, +∞)? Justify.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

See similar textbooks

Similar questions

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.
Let x1 > 1 and xn+1 = 2 − 1 / xn for n ≥ 2. Show that ( xn ) converges and find its limit.
find the limit as x approaches to infinity (x-3 / x+1)^x/a
In Example 2.4.1, show that fn(x) converges to f(x) pointwise on [0, 1]. (We haveseen the convergence at x = 0, 1.) For x ∈ [0, 1] and positive integer n, let fn(x) = xn.Then limn→∞ fn(x) = f(x),, wheref(x) = 0 if 0 ≤ x < 1,1 if x = 1.This example shows that the pointwise limit of a sequence of continuous functions need not be continuous.
The limit of (xy-2y) / (x2+y2-4x+4) as (x,y) approaches (2,0) is solved and found out that it does not exist. Can we make this continuous by defining f(2,0) = k for some real value k? If yes, what could this value be? If no, why not?
Does f(x) = 3^n+2 / 5^n converge or diverge? If it converges find the limit.
Let fn: R --> R be defined by : fn(x)= x/(1+nx2), For all n >= 1. a) Show that {fn} converges uniformly on R to a function f. b) Show that f'(x) = limn -->infinity f'n(x), For all x does not = 0, but this equality is false for x = 0. c)What assumption in the theorem on the interchange of the limit and thederivative is missing? I am stuck with that last part (C).
Prove that a function f is continuous at a limit point p iff the limit as x goes to p is f(p).
Compute the limit as x approaches infinity of x^e-x
Compute the limit of the function at −1 AND determine if the function iscontinous at 1.f (x) ={3x2 + 5, x < 15 + 2x, x ≥1
(i) Let gn(x) =1/n(1 + x2) For any fixed x ∈ R, we can see that limgn(x) = 0 so that g(x) = 0 is the pointwise limit of the sequence (gn) on R. Is this convergence uniform? The observation that 1/(1 + x2) ≤ 1 for all x ∈ R implies that .