Pertanyaan

Nilai x → 3 lim x 2 + 5 x + 6 2 x 2 + 3 x − 2 = ...

Nilai $x \to 3 lim \frac{2 x ^{2} + 3 x - 2}{x ^{2} + 5 x + 6} = ...$

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Habis dalam

Klaim

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x squared plus 3 x minus 2 over denominator x squared plus 5 x plus 6 end fraction end cell end table end style$ adalah

Pembahasan

Perhatikan perhitungan berikut. Ingat, sifat limit: Maka: Jadi, nilai adalah .

Perhatikan perhitungan berikut.

Ingat, sifat limit:

$begin mathsize 14px style limit as x rightwards arrow c of fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equals fraction numerator f open parentheses c close parentheses over denominator g open parentheses c close parentheses end fraction comma space g open parentheses c close parentheses not equal to 0 end style$

Maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator 2 x squared plus 3 x minus 2 over denominator x squared plus 5 x plus 6 end fraction end cell equals cell fraction numerator 2 open parentheses 3 close parentheses squared plus 3 open parentheses 3 close parentheses minus 2 over denominator open parentheses 3 close parentheses squared plus 5 open parentheses 3 close parentheses plus 6 end fraction end cell row blank equals cell fraction numerator 18 plus 9 minus 2 over denominator 9 plus 15 plus 6 end fraction end cell row blank equals cell 25 over 30 end cell row blank equals cell 5 over 6 end cell end table end style$

Jadi, nilai $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x squared plus 3 x minus 2 over denominator x squared plus 5 x plus 6 end fraction end cell end table end style$ adalah .