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Hitunglah nilai limit fungsi berikut!

Pertanyaan

Hitunglah nilai limit fungsi berikut!

begin mathsize 14px style limit as x rightwards arrow negative 3 of space fraction numerator x cubed plus 27 over denominator x plus 3 end fraction end style 

Pembahasan Soal:

Perhatikan pemfaktoran bentuk aljabar pangkat tiga berikut.

begin mathsize 14px style a cubed plus b cubed equals open parentheses a plus b close parentheses open parentheses a squared minus a b plus b squared close parentheses end style 

Dengan menerapkan rumus pemfaktoran di atas, limit fungsi tersebut dapat diselesaikan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 3 of space fraction numerator x cubed plus 27 over denominator x plus 3 end fraction end cell equals cell limit as x rightwards arrow negative 3 of space fraction numerator x cubed plus 3 cubed over denominator x plus 3 end fraction end cell row blank equals cell limit as x rightwards arrow negative 3 of space fraction numerator up diagonal strike open parentheses x plus 3 close parentheses end strike open parentheses x squared minus 3 x plus 9 close parentheses over denominator up diagonal strike open parentheses x plus 3 close parentheses end strike end fraction end cell row blank equals cell limit as x rightwards arrow negative 3 of space open parentheses x squared minus 3 x plus 9 close parentheses end cell row blank equals cell open parentheses negative 3 close parentheses squared minus 3 open parentheses negative 3 close parentheses plus 9 end cell row blank equals cell 9 plus 9 plus 9 end cell row blank equals 27 end table end style 

Jadi, nilai dari begin mathsize 14px style limit as x rightwards arrow negative 3 of space fraction numerator x cubed plus 27 over denominator x plus 3 end fraction end style adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 27 end table.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

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