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 :

$limit as straight x rightwards arrow straight a of invisible function application fraction numerator straight h open parentheses straight x close parentheses over denominator straight f left parenthesis straight x right parenthesis end fraction open parentheses straight f open parentheses straight x close parentheses times straight g open parentheses straight x close parentheses plus 2 straight h left parenthesis straight x right parenthesis close parentheses$

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

nilai limit dari = $limit as straight x rightwards arrow straight a of invisible function application fraction numerator straight h open parentheses straight x close parentheses over denominator straight f left parenthesis straight x right parenthesis end fraction open parentheses straight f open parentheses straight x close parentheses times straight g open parentheses straight x close parentheses plus 2 straight h left parenthesis straight x right parenthesis close parentheses$ yang nilai limit masing-masing fungsinya diketahui adalah negative 8

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 straight x rightwards arrow straight c of invisible function application kf left parenthesis straight x right parenthesis equals straight k limit as straight x rightwards arrow straight c of invisible function application straight f left parenthesis straight x right parenthesis left parenthesis ii right parenthesis space limit as straight x rightwards arrow straight c of invisible function application open square brackets straight f left parenthesis straight x right parenthesis times straight g left parenthesis straight x right parenthesis close square brackets equals open square brackets limit as straight x rightwards arrow straight c of invisible function application straight f left parenthesis straight x right parenthesis close square brackets open square brackets limit as straight x rightwards arrow straight c of invisible function application straight g left parenthesis straight x right parenthesis close square brackets left parenthesis iii right parenthesis space space limit as straight x rightwards arrow straight c of invisible function application open square brackets straight f open parentheses straight x close parentheses plus-or-minus straight g left parenthesis straight x right parenthesis close square brackets equals limit as straight x rightwards arrow straight c of invisible function application straight f left parenthesis straight x right parenthesis plus-or-minus limit as straight x rightwards arrow straight c of invisible function application straight g left parenthesis straight x right parenthesis left parenthesis iv right parenthesis space limit as straight x rightwards arrow straight c of invisible function application open square brackets fraction numerator straight f open parentheses straight x close parentheses over denominator straight g left parenthesis straight x right parenthesis end fraction close square brackets equals fraction numerator limit as straight x rightwards arrow straight c of invisible function application straight f open parentheses straight x close parentheses over denominator limit as straight x rightwards arrow straight c of invisible function application straight g open parentheses straight x close parentheses end fraction left parenthesis straight v right parenthesis space limit as straight x rightwards arrow straight c of invisible function application open square brackets straight f left parenthesis straight x right parenthesis close square brackets to the power of straight n equals open square brackets limit as straight x rightwards arrow straight c of invisible function application straight f left parenthesis straight x right parenthesis close square brackets to the power of straight n$

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 h open parentheses straight x close parentheses over denominator straight f left parenthesis straight x right parenthesis end fraction open parentheses straight f open parentheses straight x close parentheses times straight g open parentheses straight x close parentheses plus 2 straight h left parenthesis straight x right parenthesis close parentheses end cell equals cell limit as straight x rightwards arrow straight a of invisible function application open parentheses straight g open parentheses straight x close parentheses times straight h open parentheses straight x close parentheses plus 2 fraction numerator open square brackets straight h left parenthesis straight x right parenthesis close square brackets squared over denominator straight f left parenthesis straight x right parenthesis end fraction close parentheses end cell row blank equals cell limit as straight x rightwards arrow straight a of invisible function application open square brackets straight g left parenthesis straight x right parenthesis times straight h left parenthesis straight x right parenthesis close square brackets plus 2 limit as straight x rightwards arrow straight a of invisible function application open square brackets fraction numerator open square brackets straight h left parenthesis straight x right parenthesis close square brackets squared over denominator straight f left parenthesis straight x right parenthesis end fraction close square brackets end cell row blank equals cell open square brackets limit as straight x rightwards arrow straight a of invisible function application straight g left parenthesis straight x right parenthesis close square brackets times open square brackets limit as straight x rightwards arrow straight a of invisible function application straight h left parenthesis straight x right parenthesis close square brackets plus 2 fraction numerator open square brackets limit as straight x rightwards arrow straight a of invisible function application straight h left parenthesis straight x right parenthesis close square brackets squared over denominator limit as straight x rightwards arrow straight a of invisible function application straight f left parenthesis straight x right parenthesis end fraction end cell row blank equals cell open parentheses negative 3 close parentheses 4 plus 2 open parentheses 4 squared over 8 close parentheses end cell row blank equals cell negative 12 plus 2 open parentheses 16 over 8 close parentheses end cell row blank equals cell negative 12 plus 2 open parentheses 2 close parentheses end cell row blank equals cell negative 12 plus 4 end cell row blank equals cell negative 8 end cell end table$

Jadi, nilai limit dari = $limit as straight x rightwards arrow straight a of invisible function application fraction numerator straight h open parentheses straight x close parentheses over denominator straight f left parenthesis straight x right parenthesis end fraction open parentheses straight f open parentheses straight x close parentheses times straight g open parentheses straight x close parentheses plus 2 straight h left parenthesis straight x right parenthesis close parentheses$ yang nilai limit masing-masing fungsinya diketahui adalah negative 8 .

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