Pertanyaan

x → 4 lim x 2 − 2 x − 8 3 − x 2 − 7 = ...

$x \to 4 lim \frac{3 - x ^{2} - 7}{x ^{2} - 2 x - 8} = ...$

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

hasil limitnya adalah .

hasil limitnya adalah

Pembahasan

Jika disubstitusikan nilai , diperoleh bentuk tak tentu . Sehingga nilai limitnya dapat ditentukan dengan kali sekawan, Jadi, hasil limitnya adalah .

Jika disubstitusikan nilai , diperoleh bentuk tak tentu . 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 .