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Pertanyaan

Tuliskan dan tunjukkan sifat-sifat limit yang mana saja dapat digunakan untuk menyelesaikan limit fungsi berikut x → 1 lim ​ ( 2 x − 1 ) 4 !

Tuliskan dan tunjukkan sifat-sifat limit yang mana saja dapat digunakan untuk menyelesaikan limit fungsi berikut !

  1.  

  2.  

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F. Ayudhita

Master Teacher

Jawaban terverifikasi

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Pembahasan

Pembahasan
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Sifat-sifat limit yang digunakan : 1. 2. 3. 4. 5. Jadi nilai

Sifat-sifat limit yang digunakan :

1. begin mathsize 14px style limit as x rightwards arrow a of open parentheses f left parenthesis x right parenthesis close parentheses to the power of n equals open parentheses limit as x rightwards arrow a of f left parenthesis x right parenthesis close parentheses to the power of n end style

2. begin mathsize 14px style limit as x rightwards arrow a of open parentheses f left parenthesis x right parenthesis plus-or-minus g left parenthesis x right parenthesis close parentheses equals limit as x rightwards arrow a of f left parenthesis x right parenthesis plus-or-minus limit as x rightwards arrow a of g left parenthesis x right parenthesis end style

3. begin mathsize 14px style limit as x rightwards arrow a of k times f left parenthesis x right parenthesis equals k times limit as x rightwards arrow a of f left parenthesis x right parenthesis end style

4. begin mathsize 14px style limit as x rightwards arrow a of x equals a end style

5. begin mathsize 14px style limit as x rightwards arrow a of k equals k end style

 

Jadi nilai

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of left parenthesis 2 x minus 1 right parenthesis to the power of 4 end cell equals cell left parenthesis limit as x rightwards arrow 1 of left parenthesis 2 x minus 1 right parenthesis right parenthesis to the power of 4 space end cell row blank equals cell left parenthesis limit as x rightwards arrow 1 of 2 x minus limit as x rightwards arrow 1 of 1 right parenthesis to the power of 4 space end cell row blank equals cell left parenthesis 2 times limit as x rightwards arrow 1 of x minus limit as x rightwards arrow 1 of 1 right parenthesis to the power of 4 space end cell row blank equals cell left parenthesis 2 times open parentheses 1 close parentheses minus 1 right parenthesis to the power of 4 end cell row blank equals cell left parenthesis 2 minus 1 right parenthesis to the power of 4 space end cell row blank equals cell 1 to the power of 4 end cell row blank equals 1 end table end style

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