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Pertanyaan

Diketahui x → a lim ​ f ( x ) = 8 , x → a lim ​ g ( x ) = − 3 , dan x → a lim ​ h ( x ) = 4 . Tentukan: x → a lim ​ h ( x ) f ( x ) + g ( x ) ​ .

Diketahui , dan . Tentukan:

.

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D. Rajib

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Mahasiswa/Alumni Universitas Muhammadiyah Malang

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hasil dari adalah .

hasil dari begin mathsize 14px style limit as x rightwards arrow a of fraction numerator f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis over denominator h left parenthesis x right parenthesis end fraction end style adalah begin mathsize 14px style 5 over 4 end style.

Pembahasan

Ingat sifat limit bahwa dan , maka lim x → a ​ h ( x ) f ( x ) + g ( x ) ​ ​ = = = = ​ l i m x → a ​ h ( x ) l i m x → a ​ ( f ( x ) + g ( x )) ​ l i m x → a ​ h ( x ) l i m x → a ​ f ( x ) + l i m x → a ​ g ( x ) ​ 4 8 + ( − 3 ) ​ 4 5 ​ ​ Jadi hasil dari adalah .

Ingat sifat limit bahwa begin mathsize 14px 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 fraction numerator limit as x rightwards arrow a of f left parenthesis x right parenthesis over denominator limit as x rightwards arrow a of g left parenthesis x right parenthesis end fraction end style dan begin mathsize 14px style limit as x rightwards arrow a of left parenthesis f left parenthesis x right parenthesis plus-or-minus g left parenthesis x right parenthesis right parenthesis equals limit as x rightwards arrow a of f left parenthesis x right parenthesis plus-or-minus limit as x rightwards arrow a of g left parenthesis x right parenthesis end style, maka

Jadi hasil dari begin mathsize 14px style limit as x rightwards arrow a of fraction numerator f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis over denominator h left parenthesis x right parenthesis end fraction end style adalah begin mathsize 14px style 5 over 4 end style.

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