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x→4lim​x2−2x−83−x2−7​​=...

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 4 of fraction numerator 3 minus square root of x squared minus 7 end root over denominator x squared minus 2 x minus 8 end fraction equals... end style

Pembahasan:

Jika disubstitusikan nilai begin mathsize 14px style x equals 3 end style, diperoleh bentuk tak tentu begin mathsize 14px style 0 over 0 end style. Sehingga nilai limitnya dapat ditentukan dengan kali sekawan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow 4 of fraction numerator 3 minus square root of straight x squared minus 7 end root over denominator straight x squared minus 2 straight x minus 8 end fraction end cell equals cell limit as straight x rightwards arrow 4 of fraction numerator 3 minus square root of straight x squared minus 7 end root over denominator straight x squared minus 2 straight x minus 8 end fraction cross times fraction numerator 3 plus square root of straight x squared minus 7 end root over denominator 3 plus square root of straight x squared minus 7 end root end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator 9 minus open parentheses straight x squared minus 7 close parentheses over denominator open parentheses straight x squared minus 2 straight x minus 8 close parentheses open parentheses 3 plus square root of straight x squared minus 7 end root close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator 16 minus straight x squared over denominator left parenthesis straight x squared minus 2 straight x minus 8 right parenthesis left parenthesis 3 plus square root of straight x squared minus 7 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator open parentheses 4 minus straight x close parentheses open parentheses 4 plus straight x close parentheses over denominator left parenthesis straight x minus 4 right parenthesis open parentheses straight x plus 2 close parentheses left parenthesis 3 plus square root of straight x squared minus 7 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator negative left parenthesis 4 plus straight x right parenthesis over denominator open parentheses straight x plus 2 close parentheses left parenthesis 3 plus square root of straight x squared minus 7 end root right parenthesis end fraction end cell row blank equals cell fraction numerator negative left parenthesis 4 plus 4 right parenthesis over denominator open parentheses 4 plus 2 close parentheses left parenthesis 3 plus square root of 4 squared minus 7 end root right parenthesis end fraction end cell row blank equals cell fraction numerator negative 8 over denominator 6 left parenthesis 6 right parenthesis end fraction end cell row blank equals cell negative 2 over 9 end cell end table end style

Jadi, hasil limitnya adalah begin mathsize 14px style negative 2 over 9 end style.

Jawaban terverifikasi

Dijawab oleh:

H. Janatu

Mahasiswa/Alumni Universitas Riau

Terakhir diupdate 06 Oktober 2021

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