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 $x \to a lim f (x) = 8$ , $x \to a lim g (x) = - 3$ , dan $x \to a lim h (x) = 4$ . Tentukan:

$x \to a lim \frac{f ( x ) + g ( x )}{h ( x )}$ .

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D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

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

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 , maka

$lim_{x \to a} \frac{f ( x ) + g ( x )}{h ( x )} = = = = \frac{l i m _{x \to a} ( f ( x ) + g ( x ))}{l i m _{x \to a} h ( x )} \frac{l i m _{x \to a} f ( x ) + l i m _{x \to a} g ( x )}{l i m _{x \to a} h ( x )} \frac{8 + ( - 3 )}{4} \frac{5}{4}$

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 .