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Let do be the usual metric in R and let d be the mapping d: R xR R defined by S r - 1|+ y- 1| if r#y if r=y d(r, y) = Define the function f on R by f(x) = x. 1. The open ball of center 0 and radius 2 in (R, d) is a. B1 =10, 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 a, 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

Let do be the usual metric in R and let d be the mapping d: R xR R defined by S r - 1|+ y- 1| if r#y if r=y d(r, y) = Define the function f on R by f(x) = x. 1. The open ball of center 0 and radius 2 in (R, d) is a. B1 =10, 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 a, 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

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 46E: For the linear transformation from Exercise 45, let =45 and find the preimage of v=(1,1). 45. Let T...
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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(x, y) = { a – 1+|y – 1| if r#y if r =y Define the function f on R by f(x) = r. 1. The open ball of center 0 and radius 2 in (R, d) is a. B1 =10, 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 a, = 1 + 2, n > 0, then a, tends to 2 in (R, do). a. True b. False 4. The sequence a, is a Cauchy sequence in (R, d). a. True b. False 5. The sequence r, is convergent in (R, d). a. True b. False 6. f: (R, do) - (R, d) is continuous at 2. a. True b. False
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(x, y) = { a – 1+|y – 1| if r#y if r =y Define the function f on R by f(x) = r. 1. The open ball of center 0 and radius 2 in (R, d) is a. B1 =10, 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 a, = 1 + 2, n > 0, then a, tends to 2 in (R, do). a. True b. False 4. The sequence a, is a Cauchy sequence in (R, d). a. True b. False 5. The sequence r, is convergent in (R, d). a. True b. False 6. f: (R, do) - (R, d) is continuous at 2. a. True b. False
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