Pertanyaan

Jika x → a lim ( f ( x ) + g ( x ) 1 ) = 4 dan x → a lim ( f ( x ) − g ( x ) 1 ) = − 3 maka x → a lim ( ( f ( x ) 2 + ( g ( x ) 1 ) 2 ) = ...

Jika $x \to a lim (f (x) + \frac{1}{g ( x )}) = 4$ dan $x \to a lim (f (x) - \frac{1}{g ( x )}) = - 3$ maka $x \to a lim ((f (x)^{2} + (\frac{1}{g ( x )})^{2}) = ...$

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Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

$J i k a space d i p e r h a t i k a n colon limit as x rightwards arrow a of open parentheses f open parentheses x close parentheses plus fraction numerator 1 over denominator g open parentheses x close parentheses end fraction close parentheses equals 4 left right double arrow f open parentheses a close parentheses plus fraction numerator 1 over denominator g open parentheses a close parentheses end fraction equals 4 limit as x rightwards arrow a of open parentheses f open parentheses x close parentheses minus fraction numerator 1 over denominator g open parentheses x close parentheses end fraction close parentheses equals negative 3 space left right double arrow f open parentheses a close parentheses minus fraction numerator 1 over denominator g open parentheses a close parentheses end fraction equals negative 3 M i s a l colon f open parentheses a close parentheses equals p space d a n space fraction numerator 1 over denominator g open parentheses a close parentheses end fraction equals q comma space m a k a colon p plus q equals 4 fraction numerator p minus q equals negative 3 over denominator 2 p equals 1 left right double arrow p equals begin display style 1 half end style end fraction plus S e h i n g g a colon q equals 4 minus 1 half equals 7 over 2 J a d i comma space limit as x rightwards arrow a of open parentheses left parenthesis f open parentheses x close parentheses squared plus open parentheses fraction numerator 1 over denominator g open parentheses x close parentheses end fraction close parentheses squared close parentheses equals limit as x rightwards arrow a of open parentheses left parenthesis f open parentheses a close parentheses squared plus open parentheses fraction numerator 1 over denominator g open parentheses a close parentheses end fraction close parentheses squared close parentheses equals p squared plus q squared equals open parentheses 1 half close parentheses squared plus open parentheses 7 over 2 close parentheses squared equals 1 fourth plus 49 over 4 equals 50 over 4 equals 25 over 2$