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Q. 48

Found in: Page 108


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Write delta-epsilon proofs for each of the limit statements limxcfx=L in Exercises 47-60.


Delta-epsilon proof for limx23-4x=-5 is, whenever localid="1648006806212" 0<x-2<δ, we also have localid="1648021669064" 3-4x+5<ε.

See the step by step solution

Step by Step Solution

Step 1. Given information 


Step 2. Consider ε>0, choose δ=ε4.

For all x with localid="1648006934128" 0<x-2<δ,we also have localid="1648021795730" 3-4x+5<ε.

localid="1648021807616" 3-4x+5=3-4x+5 =8-4x =42-x =4x-2 <4δ =4ε4 =ε

Therefore, whenever 0<x-2<δ, we also have localid="1648021825608" 3-4x+5<ε.

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