Question

Demonstre que limx→2(−2x+7)=3limx→2(−2x+7)=3.

Answer 1

Acompanhe a definição:

$\displaystyle 0 \ \textless \ |x-a| \ \textless \ \delta \Longrightarrow |f(x) - L| \ \textless \ \epsilon \\ \\ \\ 0 \ \textless \ |x-2| \ \textless \ \delta \Longrightarrow |-2x+7-3| \ \textless \ \epsilon \\ \\ \\ 0 \ \textless \ |x-2| \ \textless \ \delta \Longrightarrow |-2x+4| \ \textless \ \epsilon \\ \\ \\ 0 \ \textless \ |x-2| \ \textless \ \delta \Longrightarrow -2 \cdot |x-2| \ \textless \ \epsilon \\ \\ \\ 0 \ \textless \ |x-2| \ \textless \ \delta \Longrightarrow |x-2| \ \textless \ - \frac{\epsilon}{2} \\ \\ \\ \boxed{\boxed{0 \ \textless \ \delta \leq - \frac{\epsilon}{2}}}$