2. f: (R. d) -→ (R, do) is cont inuous at 2 a. True b. False
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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![Let do be the usual metric in R and let d be the mapping d: R x R R defined by
d(r, y) =
|I - 1+|y- 1| if r#y
if r=y
Define the function f on R by f(x) = x.
1. The open ball of center0 and radius 2 in (R, d) is
a. B =0, 2[
b. B2= 1,2|
2. f: (R, d) - (R, do) is continuous at 2
a. True
b. False
3. Define the sequence of real numbers r
+2. n> 0, then r, tends to 2 in (R, do).
a. True
b. False
4. The sequence r, is a Cauchy sequence in (R. d).
a. True
b. False
5. The sequence r, is convergent in (R. d).
a. True
b. False
G. f: (R. do) (R.d) is contintuous at 2.
a. Irue
b. False](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1156d43f-92a9-46a9-8d4d-7ec288ce3278%2F7a8b0546-4911-4854-bbc8-41ed6c79aa2f%2Fa6z9rsz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let do be the usual metric in R and let d be the mapping d: R x R R defined by
d(r, y) =
|I - 1+|y- 1| if r#y
if r=y
Define the function f on R by f(x) = x.
1. The open ball of center0 and radius 2 in (R, d) is
a. B =0, 2[
b. B2= 1,2|
2. f: (R, d) - (R, do) is continuous at 2
a. True
b. False
3. Define the sequence of real numbers r
+2. n> 0, then r, tends to 2 in (R, do).
a. True
b. False
4. The sequence r, is a Cauchy sequence in (R. d).
a. True
b. False
5. The sequence r, is convergent in (R. d).
a. True
b. False
G. f: (R. do) (R.d) is contintuous at 2.
a. Irue
b. False
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