Find the largest delta?

Question

Find the largest delta that could be used successfully with an arbitrary e in an epsilon-delta proof of limit of (1-3x)=-5 as x approaches to 2?

 

Answer: delta=e/4

 

 

Answer 1

You want |1-3x-(-5)| < e, which means

|3(x-2)| < e

=> |x-2| < e/3

Pick δ = e/3. If |x-2| < δ, then |f(x)-(-5)| < e, where f(x) = 1-3x.

 

Answer: δmax = e/3

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Attn: My answer is different from yours.