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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 :

Diketahui  dan . 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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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 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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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 limit as straight x rightwards arrow straight a of invisible function application straight h left parenthesis straight x right parenthesis equals 4. 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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