Pertanyaan

Hitunglah setiap limit fungsi berikut. b. a → b lim a − b a a − b b

Hitunglah setiap limit fungsi berikut.

b. $a \to b lim \frac{a a - b b}{a - b}$

M. Nizar

Master Teacher

Mahasiswa/Alumni Universitas Siliwangi

Jawaban terverifikasi

Pembahasan

Untuk menemukan nilai limitnya maka dikalikan dengan akar sekawan dari penyebutnya

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as a rightwards arrow b of fraction numerator a square root of a minus b square root of b over denominator square root of a minus square root of b end fraction end cell equals cell limit as a rightwards arrow b of fraction numerator a square root of a minus b square root of b over denominator square root of a minus square root of b end fraction times fraction numerator square root of a plus square root of b over denominator square root of a plus square root of b end fraction end cell row blank equals cell limit as a rightwards arrow b of fraction numerator a squared plus a square root of a b end root minus b square root of a b end root minus b squared over denominator a minus b end fraction end cell row blank equals cell limit as a rightwards arrow b of fraction numerator a squared minus b squared plus square root of a b end root open parentheses a minus b close parentheses over denominator a minus b end fraction end cell row blank equals cell limit as a rightwards arrow b of fraction numerator a squared minus b squared over denominator a minus b end fraction plus fraction numerator square root of a b end root left parenthesis a minus b right parenthesis over denominator a minus b end fraction space space space space space comma bagi space menjadi space dua space bentuk space pecahan end cell row blank equals cell limit as a rightwards arrow b of fraction numerator up diagonal strike left parenthesis a minus b right parenthesis end strike left parenthesis a plus b right parenthesis over denominator up diagonal strike left parenthesis a minus b right parenthesis end strike end fraction plus fraction numerator square root of a b end root up diagonal strike left parenthesis a minus b right parenthesis end strike over denominator up diagonal strike left parenthesis a minus b right parenthesis end strike end fraction end cell row blank equals cell limit as a rightwards arrow b of left parenthesis a plus b right parenthesis plus square root of a b end root end cell row blank equals cell open parentheses b plus b close parentheses plus square root of b squared end root space space space comma space substitusi space nilai space a equals b end cell row blank equals cell 2 b plus b end cell row blank equals cell 3 b end cell end table end style$