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2.1 DEFINITION OF THE LIMIT OF A FUNCTION x²-4 -4 x+2 2x² + 3x - 2 x+2 1. Define f: (-2, 0)→ R by f(x) 2. Define f: (-2, 0)→ R by f(x) = Prove that f has a limit at -2, and find it. Prove that f has a limit at -2, and find it. 3. Give an example of a function ƒ : (0, 1)→ R that has a limit at every point of (0, 1) except 1. Use the definition of limit of a function to justify the example. 4. Give an example of a function f: RR that is bounded and has a limit at every point

2.1 DEFINITION OF THE LIMIT OF A FUNCTION x²-4 -4 x+2 2x² + 3x - 2 x+2 1. Define f: (-2, 0)→ R by f(x) 2. Define f: (-2, 0)→ R by f(x) = Prove that f has a limit at -2, and find it. Prove that f has a limit at -2, and find it. 3. Give an example of a function ƒ : (0, 1)→ R that has a limit at every point of (0, 1) except 1. Use the definition of limit of a function to justify the example. 4. Give an example of a function f: RR that is bounded and has a limit at every point

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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Questions 1 and 3 please
2.1 DEFINITION OF THE LIMIT OF A FUNCTION ²-4 x + 2 2x² + 3x - 2 x + 2 1. Define f: (-2, 0)→ R by f(x) = 2. Define f: (-2, 0)→ R by f(x) = Prove that f has a limit at -2, and find it. Prove that f has a limit at -2, and find it. 3. Give an example of a function f : (0, 1)→ R that has a limit at every point of (0, 1) except 1. Use the definition of limit of a function to justify the example. 4. Give an example of a function f: RR that is bounded and has a limit at every point
Transcribed Image Text:2.1 DEFINITION OF THE LIMIT OF A FUNCTION ²-4 x + 2 2x² + 3x - 2 x + 2 1. Define f: (-2, 0)→ R by f(x) = 2. Define f: (-2, 0)→ R by f(x) = Prove that f has a limit at -2, and find it. Prove that f has a limit at -2, and find it. 3. Give an example of a function f : (0, 1)→ R that has a limit at every point of (0, 1) except 1. Use the definition of limit of a function to justify the example. 4. Give an example of a function f: RR that is bounded and has a limit at every point
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