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Pertanyaan

limit as x rightwards arrow 2 of fraction numerator x squared minus 4 over denominator 2 x squared plus 4 x minus 16 end fraction equals....

Pembahasan Soal:

Perhatikan perhitungan berikut!

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x squared minus 4 over denominator 2 x squared plus 4 x minus 16 end fraction end cell equals cell fraction numerator open parentheses 2 close parentheses squared minus 4 over denominator 2 open parentheses 2 close parentheses squared plus 4 open parentheses 2 close parentheses minus 16 end fraction end cell row blank equals cell fraction numerator 4 minus 4 over denominator 8 plus 8 minus 16 end fraction end cell row blank equals cell 0 over 0 end cell end table 

Karena hasil dari limit tersebut ketika disubstitusikan x equals 2 merupakan bilangan tak tentu 0 over 0, maka kita lakukan pemfaktoran pada bentuk limit tersebut.
Dengan demikian, diperoleh hasil perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x squared minus 4 over denominator 2 x squared plus 4 x minus 16 end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x plus 2 close parentheses open parentheses x minus 2 close parentheses over denominator open parentheses 2 x plus 8 close parentheses open parentheses x minus 2 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x plus 2 close parentheses up diagonal strike open parentheses x minus 2 close parentheses end strike over denominator open parentheses 2 x plus 8 close parentheses up diagonal strike open parentheses x minus 2 close parentheses end strike end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x plus 2 close parentheses over denominator open parentheses 2 x plus 8 close parentheses end fraction end cell row blank equals cell fraction numerator 2 plus 2 over denominator 2 open parentheses 2 close parentheses plus 8 end fraction end cell row blank equals cell 4 over 12 end cell row blank equals cell 1 third end cell end table

Jadi, diperoleh bahwa limit as x rightwards arrow 2 of fraction numerator open parentheses x plus 2 close parentheses open parentheses x minus 2 close parentheses over denominator open parentheses 2 x plus 8 close parentheses open parentheses x minus 2 close parentheses end fraction equals 1 third.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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