Pertanyaan

Jika diketahui x → a lim 4 − x 2 + 7 9 − x 2 = 8 . Tentukan nilai a !

Jika diketahui $x \to a lim \frac{9 - x ^{2}}{4 - x ^{2} + 7} = 8$ . Tentukan nilai $a$ !

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai yang memenuhi adalah atau

nilai

yang memenuhi adalah a equals 3

atau

Pembahasan

Jadi, nilai yang memenuhi adalah atau

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a of fraction numerator 9 minus x squared over denominator 4 minus square root of x squared plus 7 end root end fraction times fraction numerator 4 plus square root of x squared plus 7 end root over denominator 4 plus square root of x squared plus 7 end root end fraction end cell equals 8 row cell limit as x rightwards arrow a of fraction numerator left parenthesis 9 minus x squared right parenthesis left parenthesis 4 plus square root of x squared plus 7 end root right parenthesis over denominator 16 minus left parenthesis x squared plus 7 right parenthesis end fraction end cell equals 8 row cell limit as x rightwards arrow a of fraction numerator left parenthesis 9 minus x squared right parenthesis left parenthesis 4 plus square root of x squared plus 7 end root right parenthesis over denominator 16 minus x squared minus 7 end fraction end cell equals 8 row cell limit as x rightwards arrow a of fraction numerator up diagonal strike left parenthesis 9 minus x squared right parenthesis end strike left parenthesis 4 plus square root of x squared plus 1 end root right parenthesis over denominator up diagonal strike 9 minus x squared end strike end fraction end cell equals 8 row cell 4 plus square root of a squared plus 7 end root end cell equals 8 row cell square root of a squared plus 7 end root end cell equals 4 row cell a squared plus 7 end cell equals 16 row cell a squared end cell equals 9 row a equals cell plus-or-minus square root of 9 end cell row a equals cell plus-or-minus 3 end cell end table$

Jadi, nilai yang memenuhi adalah a equals 3 atau a equals negative 3