Pertanyaan

Dengan teorema limit, hitunglah : x → 3 lim x 2 + 2 x − 3 ( x − 5 ) 3 ( 2 x − 9 )

Dengan teorema limit, hitunglah :

$x \to 3 lim \frac{( x - 5 ) ^{3} ( 2 x - 9 )}{x ^{2} + 2 x - 3}$

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Habis dalam

Klaim

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

hasildari adalah 2.

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 kembalisifat limit berikut. Dengan menggunakan konsep sifat-sifat limit kemudian dengan mensubtitusi nilai ke dalam limit fungsi tersebut. Jadi, hasildari adalah 2.

Ingat kembali sifat limit berikut.

$begin mathsize 14px style limit as straight x rightwards arrow straight c of open parentheses fraction numerator straight f open parentheses straight x close parentheses over denominator straight g open parentheses straight x close parentheses end fraction close parentheses equals fraction numerator limit as straight x rightwards arrow straight c of open parentheses straight f open parentheses straight x close parentheses close parentheses over denominator limit as straight x rightwards arrow straight c of open parentheses straight g open parentheses straight x close parentheses close parentheses end fraction end style$

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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