Question

Dengan menggunakan epsilon-delta, buktikan bahwa
limit x mendekati 4 (x^2-16)/(x-4) = 8

Answer 1

Kotretan:

Misalkan 0 < |x - 4| < δ, maka

|(x^2 - 16)/(x - 4) - 8| = |[(x + 4)(x - 4)/(x - 4)] - 8|

= |(x + 4) - 8|

= |x - 4| < ε

===

Bukti:

Ambil sebarang ε > 0

Pilih δ = ε

Sehingga, jika 0 < |x - 4| < δ, maka

|(x^2 - 16)/(x - 4) - 8| = |[(x + 4)(x - 4)/(x - 4)] - 8|

= |(x + 4) - 8|

= |x - 4| < δ = ε