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Jika x → c lim ​ f ( x ) = 6 dan x → c lim ​ g ( x ) = − 8 . Carilah setiap limit berikut. a. x → c lim ​ f 2 ( x ) − g 2 ( x ) ​

Jika . Carilah setiap limit berikut.

a.      

  1. ...space 

  2. ...undefined 

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Jawaban terverifikasi

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diperoleh .

diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow c of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of f squared left parenthesis x right parenthesis minus g squared left parenthesis x right parenthesis end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of negative 7 end root end cell end table end style.

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Sifat-sifat limit : 1. 2. 3. , asalkan Dengan menggunakan sifat-sifat limit fungsi diperoleh: Dengan demikian, diperoleh .

Sifat-sifat limit :

1. begin mathsize 14px style limit as x rightwards arrow c of open parentheses f open parentheses x close parentheses plus-or-minus g open parentheses x close parentheses close parentheses equals limit as x rightwards arrow c of f open parentheses x close parentheses plus-or-minus limit as x rightwards arrow c of g open parentheses x close parentheses end style

2. begin mathsize 14px style limit as x rightwards arrow c of f to the power of n open parentheses x close parentheses equals open parentheses limit as x rightwards arrow c of f open parentheses x close parentheses close parentheses to the power of n end style

3. begin mathsize 14px style limit as x rightwards arrow c of n-th root of f open parentheses x close parentheses end root equals n-th root of limit as x rightwards arrow c of f open parentheses x close parentheses end root end style , asalkan begin mathsize 14px style limit as x rightwards arrow c of f open parentheses x close parentheses greater or equal than 0 comma space straight n space genap end style 

Dengan menggunakan sifat-sifat limit fungsi diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow c of square root of f squared left parenthesis x right parenthesis minus g squared left parenthesis x right parenthesis end root end cell equals cell square root of limit as x rightwards arrow c of space open parentheses f squared left parenthesis x right parenthesis minus g squared left parenthesis x right parenthesis close parentheses end root end cell row blank equals cell square root of limit as x rightwards arrow c of space f squared left parenthesis x right parenthesis minus limit as x rightwards arrow c of space g squared left parenthesis x right parenthesis end root end cell row blank equals cell square root of open parentheses limit as x rightwards arrow c of space f left parenthesis x right parenthesis close parentheses squared minus open parentheses limit as x rightwards arrow c of space g left parenthesis x right parenthesis close parentheses squared end root end cell row blank equals cell square root of 6 squared minus left parenthesis negative 8 right parenthesis squared end root end cell row blank equals cell square root of 36 minus 64 end root end cell row blank equals cell square root of negative 28 end root end cell row blank equals cell 2 square root of negative 7 end root end cell end table end style 

Dengan demikian, diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow c of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of f squared left parenthesis x right parenthesis minus g squared left parenthesis x right parenthesis end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of negative 7 end root end cell end table end style.

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Konsep Kilat

Konsep Limit

Sifat Limit

Limit Fungsi Aljabar

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Diberikan x → a lim ​ f ( x ) = 3 dan x → a lim ​ g ( x ) = − 1 . Hitunglah nilai setiap limit berikut. a. x → a lim ​ f 2 ( x ) + g 2 ( x ) ​ b. x → a lim ​ f ( x ) + g ( x ) 2 f ( x ) − 3 g...

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