Pertanyaan

x → − 1 lim x 2 + 7 x + 6 x 2 − 4 x − 5 = ...

$x \to - 1 lim \frac{x ^{2} - 4 x - 5}{x ^{2} + 7 x + 6} = ...$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow negative 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared minus 4 x minus 5 over denominator x squared plus 7 x plus 6 end fraction end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 1 1 fifth close parentheses end cell end table$ .

Pembahasan

Diketahui , maka: Gunakan metode subsitusi langsung. Karena hasilnya tak tentu, dan fungsi limit merupakan fungsi kuadrat, maka gunakan metode pemfaktoran. Jadi, .

Diketahui $limit as x rightwards arrow negative 1 of fraction numerator x squared minus 4 x minus 5 over denominator x squared plus 7 x plus 6 end fraction$ , maka:

Gunakan metode subsitusi langsung.

$limit as x rightwards arrow negative 1 of fraction numerator x squared minus 4 x minus 5 over denominator x squared plus 7 x plus 6 end fraction equals fraction numerator open parentheses negative 1 close parentheses squared minus 4 times open parentheses negative 1 close parentheses minus 5 over denominator open parentheses negative 1 close parentheses squared plus 7 times open parentheses negative 1 close parentheses plus 6 end fraction equals 0 over 0 space open parentheses tak space tentu close parentheses$

Karena hasilnya tak tentu, dan fungsi limit merupakan fungsi kuadrat, maka gunakan metode pemfaktoran.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow negative 1 of fraction numerator x squared minus 4 x minus 5 over denominator x squared plus 7 x plus 6 end fraction end cell row blank equals cell limit as x rightwards arrow negative 1 of fraction numerator open parentheses x minus 5 close parentheses open parentheses x plus 1 close parentheses over denominator open parentheses x plus 6 close parentheses open parentheses x plus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 1 of fraction numerator x minus 5 over denominator x plus 6 end fraction end cell row blank equals cell fraction numerator negative 1 minus 5 over denominator negative 1 plus 6 end fraction end cell row blank equals cell fraction numerator negative 6 over denominator 5 end fraction end cell row blank equals cell negative open parentheses 1 1 fifth close parentheses end cell end table$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow negative 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared minus 4 x minus 5 over denominator x squared plus 7 x plus 6 end fraction end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 1 1 fifth close parentheses end cell end table$ .