?(a) For the \(\operatorname{limit} \lim _{x \rightarrow 1}\left(x^{3}+x+1\right)=3\)
Chapter 2, Problem 35(choose chapter or problem)
(a) For the \(\operatorname{limit} \lim _{x \rightarrow 1}\left(x^{3}+x+1\right)=3\), use a graph to find a value of \(\delta\) that corresponds to \(\varepsilon=0.4\).
(b) By solving the cubic equation \(x^{3}+x+1=3+\varepsilon\), find the largest possible value of \(\delta\) that works for any given \(\varepsilon>0\)
(c) Put \(\varepsilon=0.4\) in your answer to part (b) and compare with your answer to part (a).
Equation Transcription:
Text Transcription:
lim_x right arrow 1 (x^3+x+1)=3
delta
x^3+x+1=3+varepsilon
varepsilon=0.4
varepsilon>0
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