Pertanyaan

Latihan Tentukan nilai limit dari 3. x → 5 lim 5 − x 4 − x 2 − 9

Latihan

Tentukan nilai limit dari

$3. x \to 5 lim \frac{4 - x ^{2} - 9}{5 - x}$

D. Entry

Master Teacher

Jawaban terverifikasi

Jawaban

diperoleh nilai .

diperoleh nilai $limit as x rightwards arrow 5 of space fraction numerator 4 minus square root of x squared minus 9 end root over denominator 5 minus x end fraction equals 5 over 4$ .

Pembahasan

Perhatikan perhitungan berikut. Jadi diperoleh nilai .

Perhatikan perhitungan berikut.

$begin mathsize 14px style limit as x rightwards arrow 5 of space fraction numerator 4 minus square root of x squared minus 9 end root over denominator 5 minus x end fraction equals limit as x rightwards arrow 5 of space fraction numerator 4 minus square root of x squared minus 9 end root over denominator 5 minus x end fraction cross times fraction numerator 4 plus square root of x squared minus 9 end root over denominator 4 plus square root of x squared minus 9 end root end fraction equals limit as x rightwards arrow 5 of space fraction numerator 4 squared minus open parentheses x squared minus 9 close parentheses over denominator open parentheses 5 minus x close parentheses space open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals limit as x rightwards arrow 5 of space fraction numerator 25 minus x squared over denominator open parentheses 5 minus x close parentheses space open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals limit as x rightwards arrow 5 of space fraction numerator open parentheses 5 minus x close parentheses open parentheses 5 plus x close parentheses over denominator open parentheses 5 minus x close parentheses space open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals limit as x rightwards arrow 5 of space fraction numerator open parentheses 5 plus x close parentheses over denominator open parentheses 4 plus square root of x squared minus 9 end root close parentheses end fraction equals fraction numerator open parentheses 5 plus 5 close parentheses over denominator open parentheses 4 plus square root of 5 squared minus 9 end root close parentheses end fraction equals 10 over 8 equals 5 over 4 end style$

Jadi diperoleh nilai $limit as x rightwards arrow 5 of space fraction numerator 4 minus square root of x squared minus 9 end root over denominator 5 minus x end fraction equals 5 over 4$ .

Latihan Bab

Konsep Kilat

Konsep Limit

Sifat Limit

Limit Fungsi Aljabar