Math  /  Calculus

QuestionProve that limx8(17x+6)=507\lim _{x \rightarrow 8}\left(\frac{1}{7} x+6\right)=\frac{50}{7} by finding δ\delta in terms of ε\varepsilon.

Studdy Solution
So, we can choose δ=7ε\delta =7\varepsilon. This means that for every ε>0\varepsilon >0, if 0<x<7ε0 < |x -| <7\varepsilon, then f(x)507<ε|f(x) - \frac{50}{7}| < \varepsilon.
Therefore, δ\delta as a function of ε\varepsilon is δ(ε)=7ε\delta(\varepsilon) =7\varepsilon.

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