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Nilai x→3lim​x2+5x+62x2+3x−2​=...

Pertanyaan

Nilai begin mathsize 14px style 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 equals... end style

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

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 begin mathsize 14px style 5 over 6 end style.

Pembahasan

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 begin mathsize 14px style 5 over 6 end style.

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