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Jika x → c lim ​ f ( x ) = 6 dan x → c lim ​ g ( x ) = − 8 . Carilah setiap limit berikut. b. x → c lim ​ f ( x ) + g ( x ) 5 f ( x ) − 4 g ( x ) ​

Jika . Carilah setiap limit berikut.

b.       

  1. ...space 

  2. ...undefined 

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 begin mathsize 14px style limit as x rightwards arrow c of fraction numerator 5 f left parenthesis x right parenthesis minus 4 g left parenthesis x right parenthesis over denominator f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end fraction equals negative 31 end style.

Pembahasan

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

Sifat-sifat limit fungsi aljabar :

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 k times f open parentheses x close parentheses equals k times limit as x rightwards arrow c of f open parentheses x close parentheses end style

3. begin mathsize 14px style limit as x rightwards arrow c of fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equals fraction numerator limit as x rightwards arrow c of f open parentheses x close parentheses over denominator limit as x rightwards arrow c of g open parentheses x close parentheses end fraction end style , asalkan begin mathsize 14px style limit as x rightwards arrow c of g open parentheses x close parentheses not equal to 0 end style

Dengan menggunakan sifat-sifat limit, diperoleh:

undefined

Dengan demikian, begin mathsize 14px style limit as x rightwards arrow c of fraction numerator 5 f left parenthesis x right parenthesis minus 4 g left parenthesis x right parenthesis over denominator f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end fraction equals negative 31 end style.

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