Pertanyaan

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

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

$limit as straight x rightwards arrow straight a of invisible function application fraction numerator straight f open parentheses straight x close parentheses plus straight g open parentheses straight x close parentheses over denominator straight h open parentheses straight x close parentheses end fraction$

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

nilai limit dari yangnilai limit masing-masing fungsinya diketahui adalah .

nilai limit dari $limit as straight x rightwards arrow straight a of invisible function application fraction numerator straight f open parentheses straight x close parentheses plus straight g open parentheses straight x close parentheses over denominator straight h open parentheses straight x close parentheses end fraction$ yang nilai limit masing-masing fungsinya diketahui adalah 5 over 4

Pembahasan

Dalam menyelesaikan soal di atas, ingat sifatlimit di bawah ini. Pada soal, diketahui , dan . Maka penyelesaian soal di atas adalah Jadi, nilai limit dari yangnilai limit masing-masing fungsinya diketahui adalah .

Dalam menyelesaikan soal di atas, ingat sifat limit di bawah ini.

$left parenthesis straight i right parenthesis space limit as x rightwards arrow c of invisible function application open square brackets f open parentheses x close parentheses plus-or-minus g left parenthesis x right parenthesis close square brackets equals limit as x rightwards arrow c of invisible function application f left parenthesis x right parenthesis plus-or-minus limit as x rightwards arrow c of invisible function application g left parenthesis x right parenthesis left parenthesis ii right parenthesis space limit as x rightwards arrow c of invisible function application open square brackets fraction numerator f open parentheses x close parentheses over denominator g left parenthesis x right parenthesis end fraction close square brackets equals fraction numerator limit as x rightwards arrow c of invisible function application f left parenthesis x right parenthesis over denominator limit as x rightwards arrow c of invisible function application g left parenthesis x right parenthesis end fraction$

Pada soal, diketahui limit as straight x rightwards arrow straight a of invisible function application straight f left parenthesis straight x right parenthesis equals 8 comma blank limit as straight x rightwards arrow straight a of invisible function application straight g left parenthesis straight x right parenthesis equals negative 3 , dan . Maka penyelesaian soal di atas adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow straight a of invisible function application fraction numerator straight f open parentheses straight x close parentheses plus straight g open parentheses straight x close parentheses over denominator straight h open parentheses straight x close parentheses end fraction end cell equals cell fraction numerator limit as straight x rightwards arrow straight a of invisible function application open square brackets straight f left parenthesis straight x right parenthesis plus straight g left parenthesis straight x right parenthesis close square brackets over denominator limit as straight x rightwards arrow straight a of invisible function application straight h left parenthesis straight x right parenthesis end fraction end cell row blank equals cell fraction numerator limit as straight x rightwards arrow straight a of invisible function application straight f left parenthesis straight x right parenthesis plus limit as straight x rightwards arrow straight a of invisible function application straight g left parenthesis straight x right parenthesis over denominator limit as straight x rightwards arrow straight a of invisible function application straight h left parenthesis straight x right parenthesis end fraction end cell row blank equals cell fraction numerator 8 plus open parentheses negative 3 close parentheses over denominator 4 end fraction end cell row blank equals cell 5 over 4 end cell end table$

Jadi, nilai limit dari $limit as straight x rightwards arrow straight a of invisible function application fraction numerator straight f open parentheses straight x close parentheses plus straight g open parentheses straight x close parentheses over denominator straight h open parentheses straight x close parentheses end fraction$ yang nilai limit masing-masing fungsinya diketahui adalah 5 over 4 .

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