Tentukan nilai x→5lim x−5x−5=....

Pertanyaan

Tentukan nilai $begin mathsize 14px style limit as x rightwards arrow 5 of space fraction numerator square root of x minus square root of 5 over denominator x minus 5 end fraction equals.... end style$

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

$begin mathsize 14px style limit as x rightwards arrow 5 of space fraction numerator square root of x minus square root of 5 over denominator x minus 5 end fraction equals 1 over 10 square root of 5 end style$ .

Pembahasan

$begin mathsize 14px style limit as x rightwards arrow 5 of space fraction numerator square root of x minus square root of 5 over denominator x minus 5 end fraction equals limit as x rightwards arrow 5 of space fraction numerator square root of x minus square root of 5 over denominator x minus 5 end fraction times fraction numerator square root of x plus square root of 5 over denominator square root of x plus square root of 5 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 equals limit as x rightwards arrow 5 of space fraction numerator x minus 5 over denominator open parentheses x minus 5 close parentheses open parentheses square root of x plus square root of 5 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 equals limit as x rightwards arrow 5 of space fraction numerator 1 over denominator square root of x plus square root of 5 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 equals fraction numerator 1 over denominator square root of 5 plus square root of 5 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 equals fraction numerator 1 over denominator 2 square root of 5 end fraction times fraction numerator square root of 5 over denominator square root of 5 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 equals fraction numerator square root of 5 over denominator 2 times 5 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 equals fraction numerator square root of 5 over denominator 10 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 equals 1 over 10 square root of 5 end style$

Jadi, $begin mathsize 14px style limit as x rightwards arrow 5 of space fraction numerator square root of x minus square root of 5 over denominator x minus 5 end fraction equals 1 over 10 square root of 5 end style$ .