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Asked Oct 22, 2019
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Exercise 1: Provide an e-6 proof for the following limits
(a) lim 33x21
r+3
(b) lim 2-1|
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Exercise 1: Provide an e-6 proof for the following limits (a) lim 33x21 r+3 (b) lim 2-1|

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Expert Answer

Step 1

To establish the limits of the function using epsilon -delta definition

Step 2

The epsilon -delta definition of the limit of a function f(x) at x=a

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Definition Limit f(x), as x -»a is L if given s 0,38 > 0,such that \f(x)-L<6,whenever x -a k8

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Step 3

a) f(x) =x^3-3x^2+1, x = 3, L =1 (=f(3)=27-27+1, in fact f(x) is continuous...

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f(x) increases at x-3(see graph) Suffices to look for 8,with (3+ -3(3++1-1<8 83 +68 +98< E. Take & 1, so that 8 <82 <8 168 <E. So, take 8 0,with 8 = , say 17 16 (then,168 <8) 17

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Math

Calculus

Limits

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