Prove the following limit statement using the formal definition of a limit. lim

Question

Prove the following limit statement using the formal definition of a limit. lim x rightarrow 3(x^2 - 6x + 28) = 19. That is, given any epsilon > 0, find the largest value of delta > 0 so that the formal definition of the limit holds. ANSWER: Delta = Type eps for epsilon (it must be typed in lower case letters). For example, if your answer is delta = 2epsilon + 3, then in the box would type 2*eps+3 IMPORTANT: Make sure you know how to JUSTIFY that your choice of delta satisfies the conditions given above.

Explanation / Answer

epsilon delta defination :

if limx->af(x)=L

|f(x)) -L|< ,|x-a|< , 0<<1 ,>0,>0

limx->3(x2-6x+28) =19

|(x2-6x+28) -19|<

|x2-6x+9|<

|(x-3)2|<

|x-3|<

=E

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