Roboguru

Tentukan nilai x→6lim​x−63x−2​−2x+4​​=....

Pertanyaan

Tentukan nilai begin mathsize 14px style limit as x rightwards arrow 6 of space fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction equals.... end style 

Pembahasan Soal:

begin mathsize 14px style limit as x rightwards arrow 6 of space fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction equals limit as x rightwards arrow 6 of space fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction times fraction numerator square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root over denominator square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root 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 space space space space space space space space space space space space space equals limit as x rightwards arrow 6 of space fraction numerator open parentheses 3 x minus 2 close parentheses minus open parentheses 2 x plus 4 close parentheses over denominator open parentheses x minus 6 close parentheses open parentheses square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root 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 space space space space space space space space space space space space space equals limit as x rightwards arrow 6 of space fraction numerator 3 x minus 2 minus 2 x minus 4 over denominator left parenthesis x minus 6 right parenthesis left parenthesis square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root right parenthesis 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 space space space space space space space space space space space space space equals limit as x rightwards arrow 6 of space fraction numerator x minus 6 over denominator left parenthesis x minus 6 right parenthesis left parenthesis square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root right parenthesis 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 space space space space space space space space space space space space space equals limit as x rightwards arrow 6 of space fraction numerator 1 over denominator left parenthesis square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root right parenthesis 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 space space space space space space space space space space space space space equals fraction numerator 1 over denominator left parenthesis square root of 3 open parentheses 6 close parentheses minus 2 end root plus square root of 2 open parentheses 6 close parentheses plus 4 end root right parenthesis 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 space space space space space space space space space space space space space equals fraction numerator 1 over denominator left parenthesis square root of 18 minus 2 end root plus square root of 12 plus 4 end root right parenthesis 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 space space space space space space space space space space space space space equals fraction numerator 1 over denominator left parenthesis square root of 16 plus square root of 16 right parenthesis 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 space space space space space space space space space space space space space equals fraction numerator 1 over denominator left parenthesis 4 plus 4 right parenthesis 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 space space space space space space space space space space space space space equals 1 over 8 end style  

Jadi, begin mathsize 14px style limit as x rightwards arrow 6 of space fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction equals 1 over 8 end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

W. Lestari

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 06 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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