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Jika diketahui x → c lim ​ f ( x ) = 5 dan x → c lim ​ g ( x ) = 8 Maka nilai dari x → c lim ​ [ f ( x ) ] 2 − 2 g ( x ) ​ = ...

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H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

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diperoleh nilai limit tersebut adalah .

diperoleh nilai limit tersebut adalah 3.

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Pembahasan

Ingat sifat-sifat limit berikut : Berdasarkan sifat-sifat tersebut, maka Jadi, diperoleh nilai limit tersebut adalah .

Ingat sifat-sifat limit berikut :

rightwards double arrow limit as x rightwards arrow c of straight k g left parenthesis x right parenthesis equals straight k limit as x rightwards arrow c of g left parenthesis x right parenthesis rightwards double arrow limit as x rightwards arrow c of open square brackets f left parenthesis x right parenthesis plus-or-minus g left parenthesis x right parenthesis close square brackets equals limit as x rightwards arrow c of f left parenthesis x right parenthesis plus-or-minus limit as x rightwards arrow c of g left parenthesis x right parenthesis rightwards double arrow limit as x rightwards arrow c of open square brackets f left parenthesis x right parenthesis close square brackets to the power of n equals open square brackets limit as x rightwards arrow c of f left parenthesis x right parenthesis close square brackets to the power of n

Berdasarkan sifat-sifat tersebut, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow c of square root of open square brackets f left parenthesis x right parenthesis close square brackets squared minus 2 g left parenthesis x right parenthesis end root end cell equals cell square root of limit as x rightwards arrow c of open parentheses open square brackets f left parenthesis x right parenthesis close square brackets squared minus 2 g left parenthesis x right parenthesis close parentheses end root end cell row blank equals cell square root of open square brackets limit as x rightwards arrow c of f left parenthesis x right parenthesis close square brackets squared minus 2 limit as x rightwards arrow c of g left parenthesis x right parenthesis end root end cell row blank equals cell square root of 5 squared minus 2 left parenthesis 8 right parenthesis end root end cell row blank equals cell square root of 9 end cell row blank equals 3 end table

Jadi, diperoleh nilai limit tersebut adalah 3.

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