Pertanyaan

Tentukan nilai limit fungsi berikut: x → 2 lim 3 − x 2 + 5 4 − x 2

Tentukan nilai limit fungsi berikut:

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

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 2 of fraction numerator 4 minus x squared over denominator 3 minus square root of x squared plus 5 end root end fraction end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator 4 minus x squared over denominator 3 minus square root of x squared plus 5 end root end fraction cross times fraction numerator 3 plus square root of x squared plus 5 end root over denominator 3 plus square root of x squared plus 5 end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator open parentheses 4 minus x squared close parentheses open parentheses 3 plus square root of x squared plus 5 end root close parentheses over denominator 9 minus open parentheses x squared plus 5 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator up diagonal strike open parentheses 4 minus x squared close parentheses end strike open parentheses 3 plus square root of x squared plus 5 end root close parentheses over denominator up diagonal strike open parentheses 4 minus x squared close parentheses end strike end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses 3 plus square root of x squared plus 5 end root close parentheses end cell row blank equals cell 3 plus square root of 2 squared plus 5 end root end cell row blank equals cell 3 plus square root of 9 end cell row blank equals cell 3 plus 3 end cell row blank equals 6 end table end style$