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Dengan teorema limit, hitunglah :
 

begin mathsize 14px style limit as straight x rightwards arrow negative 2 of open parentheses straight x plus 4 close parentheses open parentheses straight x squared plus 3 straight x minus 5 close parentheses end style 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

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Pembahasan

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 cross times straight g open parentheses straight x close parentheses close parentheses equals limit as straight x rightwards arrow straight c of open parentheses straight f open parentheses straight x close parentheses close parentheses cross times limit as straight x rightwards arrow straight c of open parentheses straight g open parentheses straight x close parentheses close parentheses end style 
 

maka pada begin mathsize 14px style limit as straight x rightwards arrow negative 2 of open parentheses straight x plus 4 close parentheses open parentheses straight x squared plus 3 straight x minus 5 close parentheses end style diubah bentuk menjadi
 

begin mathsize 14px style limit as straight x rightwards arrow negative 2 of open parentheses straight x plus 4 close parentheses cross times limit as straight x rightwards arrow negative 2 of open parentheses straight x squared plus 3 straight x minus 5 close parentheses 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 
 

Diperoleh :

 

begin mathsize 14px style limit as straight x rightwards arrow negative 2 of open parentheses straight x plus 4 close parentheses cross times limit as straight x rightwards arrow negative 2 of open parentheses straight x squared plus 3 straight x minus 5 close parentheses equals open parentheses limit as straight x rightwards arrow negative 2 of open parentheses straight x close parentheses plus limit as straight x rightwards arrow negative 2 of open parentheses 4 close parentheses close parentheses cross times open parentheses limit as straight x rightwards arrow negative 2 of open parentheses straight x squared close parentheses plus limit as straight x rightwards arrow negative 2 of open parentheses 3 straight x close parentheses plus limit as straight x rightwards arrow negative 2 of open parentheses 5 close parentheses close parentheses equals open parentheses negative 2 plus 4 close parentheses cross times open parentheses open parentheses negative 2 close parentheses squared plus 3 open parentheses negative 2 close parentheses minus 5 close parentheses equals 2 cross times open parentheses 4 minus 6 minus 5 close parentheses equals 2 cross times open parentheses negative 7 close parentheses equals negative 14 end style 
 

Jadi, begin mathsize 14px style limit as straight x rightwards arrow negative 2 of open parentheses straight x plus 4 close parentheses open parentheses straight x squared plus 3 straight x minus 5 close parentheses equals negative 14 end style 

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