Nilaix→−3lim​(x+312​+x2−972​) adalah ...

Pertanyaan

Nilaibegin mathsize 14px style limit as x rightwards arrow negative 3 of open parentheses fraction numerator 12 over denominator x plus 3 end fraction plus fraction numerator 72 over denominator x squared minus 9 end fraction close parentheses end style adalah ... 

F. Juliano

Master Teacher

Jawaban terverifikasi

Jawaban

nilai limit dari begin mathsize 14px style limit as x rightwards arrow negative 3 of open parentheses fraction numerator 12 over denominator x plus 3 end fraction plus fraction numerator 72 over denominator x squared minus 9 end fraction close parentheses end style adalah negative 2.

Pembahasan

Tentukanlah nilai limit dengan cara mensubstitusikan nilai limitnya terlebih dahulu:
 

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 3 of open parentheses fraction numerator 12 over denominator x plus 3 end fraction plus fraction numerator 72 over denominator x squared minus 9 end fraction close parentheses end cell equals cell fraction numerator 12 over denominator left parenthesis negative 3 right parenthesis plus 3 end fraction plus fraction numerator 72 over denominator left parenthesis negative 3 right parenthesis squared minus 9 end fraction end cell row blank equals cell 12 over 0 plus 72 over 0 end cell end table
 

Karena penyebutnya 0 maka gunakan cara yang lain untuk menentukan nilai limitnya.
 

 begin mathsize 14px style limit as x rightwards arrow negative 3 of open parentheses fraction numerator 12 over denominator x plus 3 end fraction plus fraction numerator 72 over denominator x squared minus 9 end fraction close parentheses equals limit as x rightwards arrow negative 3 of open parentheses fraction numerator 12 open parentheses x minus 3 close parentheses plus 72 over denominator open parentheses x plus 3 close parentheses open parentheses x minus 3 close parentheses end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow negative 3 of open parentheses fraction numerator 12 x minus 36 plus 72 over denominator open parentheses x plus 3 close parentheses open parentheses x minus 3 close parentheses end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow negative 3 of open parentheses fraction numerator 12 x plus 36 over denominator open parentheses x plus 3 close parentheses open parentheses x minus 3 close parentheses end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow negative 3 of open parentheses fraction numerator 12 open parentheses x plus 3 close parentheses over denominator open parentheses x plus 3 close parentheses open parentheses x minus 3 close parentheses end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 12 over denominator negative 3 minus 3 end fraction equals negative 2 end style 
 

Dengan demikian, nilai limit dari begin mathsize 14px style limit as x rightwards arrow negative 3 of open parentheses fraction numerator 12 over denominator x plus 3 end fraction plus fraction numerator 72 over denominator x squared minus 9 end fraction close parentheses end style adalah negative 2.

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