Pertanyaan

Nilai x → 2 lim x − 2 x 2 − 2 = ...

Nilai $x \to 2 lim \frac{x ^{2} - 2}{x - 2}$ = ...

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Habis dalam

Klaim

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Ingat! Tip! Gunakan Dalil L'Hospital

Ingat!

$begin mathsize 12px style limit as x rightwards arrow square root of 2 of fraction numerator x squared minus 2 over denominator x minus square root of 2 end fraction equals limit as x rightwards arrow square root of 2 of fraction numerator x squared minus open parentheses square root of 2 close parentheses squared over denominator x minus square root of 2 end fraction equals limit as x rightwards arrow square root of 2 of fraction numerator open parentheses x plus square root of 2 close parentheses open parentheses x minus square root of 2 close parentheses over denominator x minus square root of 2 end fraction equals limit as x rightwards arrow square root of 2 of open parentheses x plus square root of 2 close parentheses equals square root of 2 plus square root of 2 equals 2 square root of 2 end style$

Tip!

Gunakan Dalil L'Hospital

$begin mathsize 12px style limit as x rightwards arrow a of fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals limit as x rightwards arrow a of fraction numerator begin display style f apostrophe left parenthesis x right parenthesis end style over denominator begin display style g apostrophe left parenthesis x right parenthesis end style end fraction equals fraction numerator begin display style f apostrophe left parenthesis a right parenthesis end style over denominator begin display style g apostrophe left parenthesis a right parenthesis end style end fraction limit as x rightwards arrow a of fraction numerator begin display style x squared minus 2 end style over denominator begin display style x minus square root of 2 end style end fraction equals limit as x rightwards arrow a of fraction numerator begin display style 2 x end style over denominator begin display style 1 end style end fraction equals fraction numerator begin display style 2 end style square root of 2 over denominator 1 end fraction equals 2 square root of 2 end style$