Pertanyaan

N i l ai d a r i x → 2 lim x 2 − 2 x x 2 − x − 2 a d a l ah ...

$N i l ai d a r i x \to 2 lim \frac{x ^{2} - x - 2}{x ^{2} - 2 x} a d a l ah ...$

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A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

$D a l a m space m e n e n t u k a n space n i l a i space limit as x rightwards arrow a of fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction space y a n g space m e n g h a s i l k a n space b e n t u k space t a k space t e n t u space open parentheses 0 over 0 close parentheses space d a p a t space d i g u n a k a n space t e o r e m a space L apostrophe H o s p i t a l comma space y a i t u colon limit as x rightwards arrow a of fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals limit as x rightwards arrow a of fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction D e n g a n space f apostrophe left parenthesis x right parenthesis equals space t u r u n a n space p e r t a m a space f left parenthesis x right parenthesis space d a n space g apostrophe left parenthesis x right parenthesis equals t u r u n a n space p e r t a m a space g left parenthesis x right parenthesis limit as x rightwards arrow 2 of fraction numerator x squared minus x minus 2 over denominator x squared minus 2 x end fraction equals limit as x rightwards arrow 2 of fraction numerator 2 x minus 1 over denominator 2 x minus 2 end fraction equals fraction numerator 2 left parenthesis 2 right parenthesis minus 1 over denominator 2 left parenthesis 2 right parenthesis minus 2 end fraction equals fraction numerator 4 minus 1 over denominator 4 minus 2 end fraction equals 3 over 2 equals 1 1 half$