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Pertanyaan

Dengan teorema limit, hitunglah : x → 1 lim ​ ( x 2 − 3 ) 5

Dengan teorema limit, hitunglah :
 

  

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R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Jawaban

nilai

nilai begin mathsize 14px style limit as straight x rightwards arrow 1 of open parentheses straight x squared minus 3 close parentheses to the power of 5 equals negative 32 end style  

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Pembahasan

Dengan menggunakan konsep : maka pada diubah bentuk menjadi Kemudian ingat bahwa Maka kita ubah bentuk limit menjadi konsep di atas dan evaluasi limit dengan mensubtitusi nilai ke dalam pernyataan tersebut : Jadi, nilai

Dengan menggunakan konsep :
 

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

maka pada begin mathsize 14px style limit as straight x rightwards arrow 1 of open parentheses straight x squared minus 3 close parentheses to the power of 5 end style diubah bentuk menjadi

begin mathsize 14px style open parentheses limit as straight x rightwards arrow 1 of open parentheses straight x squared minus 3 close parentheses close parentheses to the power of 5 end style  

Kemudian ingat bahwa

 

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

Maka kita ubah bentuk limit menjadi konsep di atas dan evaluasi limit dengan mensubtitusi nilai begin mathsize 14px style straight x end style ke dalam pernyataan tersebut :

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as straight x rightwards arrow 1 of open parentheses straight x squared minus 3 close parentheses to the power of 5 end cell equals cell open parentheses limit as straight x rightwards arrow 1 of open parentheses straight x squared minus 3 close parentheses close parentheses to the power of 5 end cell row blank equals cell open parentheses limit as straight x rightwards arrow 1 of open parentheses straight x squared close parentheses minus limit as straight x rightwards arrow 1 of open parentheses 3 close parentheses close parentheses to the power of 5 end cell row blank equals cell open parentheses limit as straight x rightwards arrow 1 of open parentheses straight x squared close parentheses minus 3 close parentheses to the power of 5 end cell row blank equals cell open parentheses 1 squared minus 3 close parentheses to the power of 5 end cell row blank equals cell open parentheses negative 2 close parentheses to the power of 5 end cell row blank equals cell negative 32 end cell end table end style  
 

Jadi, nilai begin mathsize 14px style limit as straight x rightwards arrow 1 of open parentheses straight x squared minus 3 close parentheses to the power of 5 equals negative 32 end style  

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