Buktikan bahwa limit x mendekati 0 (2x-1) = -1

Materi Limit

[tex] \displaystyle \lim_{x \to 0} (2x-1)= -1 [/tex]
Analisis epsilon
[tex] \displaystyle |f(x) - L| = |2x-1 -(-1)| \\ = |2x| = 2 |x| < \epsilon \\ |x| < \frac{\epsilon}{2} [/tex]

Ambil
[tex] \delta = \frac{\epsilon}{2} \\ \text{dan} \\ |x-0| = |x| < \delta \\ \text{mengakibatkan,} \\
|f(x) - L| = |2x| = 2|x| < 2\delta = \epsilon [/tex]

Terbukti sesuai dgn definisi presisi limit.