Nilai dari x→2lim​x2+x−63x2−x−10​ adalah ...

Pertanyaan

Nilai dari begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator 3 x squared minus x minus 10 over denominator x squared plus x minus 6 end fraction end style adalah ...

 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

nilai limitnya adalah begin mathsize 14px style 11 over 5 end style

Pembahasan

Bila kita gunakan cara substitusi, maka kita akan mendapatkan bentuk limit tak tentu. Oleh karena itu, kita gunakan cara pemfaktoran.

begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator 3 x squared minus x minus 10 over denominator x squared plus x minus 6 end fraction equals limit as x rightwards arrow 2 of fraction numerator open parentheses 3 x plus 5 close parentheses open parentheses x minus 2 close parentheses over denominator open parentheses x plus 3 close parentheses open parentheses x minus 2 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow 2 of fraction numerator open parentheses 3 x plus 5 close parentheses over denominator open parentheses x plus 3 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 3 open parentheses 2 close parentheses plus 5 over denominator 2 plus 3 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 11 over 5 end style 

Jadi, nilai limitnya adalah begin mathsize 14px style 11 over 5 end style

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Tentukan nilai limit dari fungsi-fungsi berikut ini: x→1lim​x−1x​−1​

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