Pertanyaan

Nilai x → 2 lim ( x 2 − 4 2 − x 2 + 2 x − 8 3 ) = …

Nilai $x \to 2 lim (\frac{2}{x ^{2} - 4} - \frac{3}{x ^{2} + 2 x - 8}) = \dots$

H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

nilai limit tersebut adalah .

nilai limit tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 24 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 24 end cell end table

Pembahasan

Lakukan pengurangan dengan menyamakan penyebut. Kemudian limit dapat dicari menggunakan substitusi. Jadi, nilai limit tersebut adalah .

Lakukan pengurangan dengan menyamakan penyebut. Kemudian limit dapat dicari menggunakan substitusi.

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of open parentheses fraction numerator 2 over denominator x squared minus 4 end fraction minus fraction numerator 3 over denominator x squared plus 2 x minus 8 end fraction close parentheses end cell equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator 2 over denominator open parentheses x minus 2 close parentheses open parentheses x plus 2 close parentheses end fraction minus fraction numerator 3 over denominator open parentheses x plus 4 close parentheses open parentheses x minus 2 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator 2 open parentheses x plus 4 close parentheses minus 3 open parentheses x plus 2 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses x plus 2 close parentheses open parentheses x plus 4 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator 2 x plus 8 minus 3 x minus 6 over denominator open parentheses x minus 2 close parentheses open parentheses x plus 2 close parentheses open parentheses x plus 4 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator negative x plus 2 over denominator open parentheses x minus 2 close parentheses open parentheses x plus 2 close parentheses open parentheses x plus 4 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator negative open parentheses x minus 2 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses x plus 2 close parentheses open parentheses x plus 4 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator negative 1 over denominator open parentheses x plus 2 close parentheses open parentheses x plus 4 close parentheses end fraction close parentheses end cell row blank equals cell fraction numerator negative 1 over denominator open parentheses 2 plus 2 close parentheses open parentheses 2 plus 4 close parentheses end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 4 times 6 end fraction end cell row blank equals cell negative 1 over 24 end cell end table$

Jadi, nilai limit tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 24 end cell end table .