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Dengan teorema limit, hitunglah :
 

begin mathsize 14px style limit as straight x rightwards arrow 3 of fraction numerator open parentheses straight x minus 5 close parentheses cubed open parentheses 2 straight x minus 9 close parentheses over denominator straight x squared plus 2 straight x minus 3 end fraction end style  

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

hasil dari begin mathsize 14px style limit as straight x rightwards arrow 3 of fraction numerator open parentheses straight x minus 5 close parentheses cubed open parentheses 2 straight x minus 9 close parentheses over denominator straight x squared plus 2 straight x minus 3 end fraction end style adalah 2.

Pembahasan

Ingat kembali sifat limit berikut.

  1. begin mathsize 14px style limit as straight x rightwards arrow straight c of open parentheses fraction numerator straight f open parentheses straight x close parentheses over denominator straight g open parentheses straight x close parentheses end fraction close parentheses equals fraction numerator limit as straight x rightwards arrow straight c of open parentheses straight f open parentheses straight x close parentheses close parentheses over denominator limit as straight x rightwards arrow straight c of open parentheses straight g open parentheses straight x close parentheses close parentheses end fraction end style 
  2. begin mathsize 14px style limit as straight x rightwards arrow straight c of open parentheses straight f open parentheses straight x close parentheses cross times straight g open parentheses straight x close parentheses close parentheses equals limit as straight x rightwards arrow straight c of open parentheses straight f open parentheses straight x close parentheses close parentheses cross times limit as straight x rightwards arrow straight c of open parentheses straight g open parentheses straight x close parentheses close parentheses end style 
  3. begin mathsize 14px style limit as straight x rightwards arrow straight c of open parentheses straight f open parentheses straight x close parentheses plus-or-minus straight g open parentheses straight x close parentheses close parentheses equals limit as straight x rightwards arrow straight c of straight f open parentheses straight x close parentheses plus-or-minus limit as straight x rightwards arrow straight c of straight g open parentheses straight x close parentheses end style
  4. begin mathsize 14px style limit as straight x rightwards arrow straight c of straight k times straight f open parentheses straight x close parentheses equals straight k times limit as straight x rightwards arrow straight c of straight f open parentheses straight x close parentheses end style
  5. begin mathsize 14px style limit as straight x rightwards arrow straight c of open parentheses straight k close parentheses equals straight k end style  

Dengan menggunakan konsep sifat-sifat limit kemudian dengan mensubtitusi nilai straight x ke dalam limit fungsi tersebut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow 3 of fraction numerator open parentheses straight x minus 5 close parentheses cubed open parentheses 2 straight x minus 9 close parentheses over denominator straight x squared plus 2 straight x minus 3 end fraction end cell row blank equals cell fraction numerator open parentheses limit as straight x rightwards arrow 3 of open parentheses straight x close parentheses minus limit as straight x rightwards arrow 3 of open parentheses 5 close parentheses close parentheses cubed cross times open parentheses 2 cross times limit as straight x rightwards arrow 3 of open parentheses straight x close parentheses minus limit as straight x rightwards arrow 3 of open parentheses 9 close parentheses close parentheses over denominator open parentheses limit as straight x rightwards arrow 3 of open parentheses straight x close parentheses close parentheses squared plus open parentheses 2 cross times limit as straight x rightwards arrow 3 of open parentheses straight x close parentheses close parentheses minus limit as straight x rightwards arrow 3 of open parentheses 3 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 3 minus 5 close parentheses cubed cross times open parentheses open parentheses 2 straight x 3 close parentheses minus 9 close parentheses over denominator 3 squared plus open parentheses 2 cross times 3 close parentheses minus 3 end fraction end cell row blank equals cell fraction numerator open parentheses negative 8 close parentheses cross times open parentheses negative 3 close parentheses over denominator 12 end fraction end cell row blank equals 2 end table 
 

Jadi, hasil dari begin mathsize 14px style limit as straight x rightwards arrow 3 of fraction numerator open parentheses straight x minus 5 close parentheses cubed open parentheses 2 straight x minus 9 close parentheses over denominator straight x squared plus 2 straight x minus 3 end fraction end style adalah 2.

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