Tentukan nilai limit berikut! x→9limx2−14x+45x+2x−15

Tentukan nilai limit berikut! x→9limx2−14x+45x+...

Pertanyaan

Tentukan nilai limit berikut!

$begin mathsize 14px style limit as x rightwards arrow 9 of fraction numerator x plus 2 square root of x minus 15 over denominator x squared minus 14 x plus 45 end fraction end style$

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L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 9 of fraction numerator x plus 2 square root of x minus 15 over denominator x squared minus 14 x plus 45 end fraction end cell equals cell limit as x rightwards arrow 9 of fraction numerator open parentheses square root of x minus 3 close parentheses open parentheses square root of x plus 5 close parentheses over denominator open parentheses x minus 9 close parentheses open parentheses x minus 5 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 9 of fraction numerator open parentheses square root of x minus 3 close parentheses open parentheses square root of x plus 5 close parentheses over denominator open parentheses square root of x minus 3 close parentheses open parentheses square root of x plus 3 close parentheses open parentheses x minus 5 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 9 of fraction numerator square root of x plus 5 over denominator open parentheses square root of x plus 3 close parentheses open parentheses x minus 5 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 9 plus 5 over denominator open parentheses square root of 9 plus 3 close parentheses open parentheses 9 minus 5 close parentheses end fraction end cell row blank equals cell 8 over 24 end cell row blank equals cell 1 third end cell end table end style$

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