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Match three of the below statements to the definition of f that makes them true, and identify the statement that is never true. -- ✓ is not true of any function z2+5£ £<-1 x=-1 x>-1 - is true if f(x) = -4 3x - 1 x² + 4x +4 x < −1 x= -1 x>-1 - ✓ is true if f(x) = -3 x+2 x² + 4x 1 x < −1 x= -1 x>-1 -- ✓ is true if f(x) = 0 3x+8 1. The limit lim→→1 f(x) exists but the function is not continuous at x = -1 2. The limit limx→-1 f(x) does not exist but the function is continuous at x = -1 3. The limit lim→-1 f(x) exists and the function is continuous at x = -1 4. The limit lim-1 f(x) does not exist and the function is not continuous at x = -1

Match three of the below statements to the definition of f that makes them true, and identify the statement that is never true. -- ✓ is not true of any function z2+5£ £<-1 x=-1 x>-1 - is true if f(x) = -4 3x - 1 x² + 4x +4 x < −1 x= -1 x>-1 - ✓ is true if f(x) = -3 x+2 x² + 4x 1 x < −1 x= -1 x>-1 -- ✓ is true if f(x) = 0 3x+8 1. The limit lim→→1 f(x) exists but the function is not continuous at x = -1 2. The limit limx→-1 f(x) does not exist but the function is continuous at x = -1 3. The limit lim→-1 f(x) exists and the function is continuous at x = -1 4. The limit lim-1 f(x) does not exist and the function is not continuous at x = -1

Advanced Engineering Mathematics
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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Match three of the below statements to the definition ff that makes them true, and identify the statement that is never true. -- ✓ is not true of any function 2 -4 3x - 1 ✓ is true if f(x) = = +52 x<-1 x = -1 x>-1 ✓ is true if f(x)= = x² + 4x +4 x < -1 2 x = -1 x>-1 ✓is true if f(x) = { −3 x + 2 2 x² + 4x 1 0 3x + 8 x < -1 x = -1 x>-1 1. The limit lim1 f(x) exists but the function is not continuous at x = -1 2. The limit lim→-1 f(x) does not exist but the function is continuous at x = -1 3. The limit lim→-1 f(x) exists and the function is continuous at x = −1 4. The limit lim→-1 f(x) does not exist and the function is not continuous at x = −1
Transcribed Image Text:Match three of the below statements to the definition ff that makes them true, and identify the statement that is never true. -- ✓ is not true of any function 2 -4 3x - 1 ✓ is true if f(x) = = +52 x<-1 x = -1 x>-1 ✓ is true if f(x)= = x² + 4x +4 x < -1 2 x = -1 x>-1 ✓is true if f(x) = { −3 x + 2 2 x² + 4x 1 0 3x + 8 x < -1 x = -1 x>-1 1. The limit lim1 f(x) exists but the function is not continuous at x = -1 2. The limit lim→-1 f(x) does not exist but the function is continuous at x = -1 3. The limit lim→-1 f(x) exists and the function is continuous at x = −1 4. The limit lim→-1 f(x) does not exist and the function is not continuous at x = −1
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