Math  /  Calculus

QuestionFind the largest δ\delta for ε=0.2\varepsilon=0.2 and ε=0.1\varepsilon=0.1 in the limit limx2(x35x+5)=3\lim _{x \rightarrow 2}(x^{3}-5 x+5)=3. Round to four decimal places.

Studdy Solution
Calculate the value of δ\delta for ε=0.\varepsilon=0..
δ=min(2.9572,22.0428)0.0428\delta = \min(|2 -.9572|, |2 -2.0428|) \approx0.0428So, the largest possible values of δ\delta that correspond to ε=0.2\varepsilon=0.2 and ε=0.\varepsilon=0. are approximately 0.08550.0855 and 0.04280.0428 respectively.
ε=0.2δ=0.0855ε=0.δ=0.0428\begin{array}{ll} \varepsilon=0.2 & \delta=0.0855 \\ \varepsilon=0. & \delta=0.0428\end{array}

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