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Tentukan nilai imit masing-masing fungsi rasional berikut.  c. s→1lim​s−1s3−1​

Pertanyaan

Tentukan nilai imit masing-masing fungsi rasional berikut. 

c. begin mathsize 14px style limit as s rightwards arrow 1 of fraction numerator s cubed minus 1 over denominator s minus 1 end fraction end style        

S. Indah

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

nilai limit as s rightwards arrow 1 of fraction numerator s cubed minus 1 over denominator s minus 1 end fraction equals 3.

Pembahasan

Carilah nilai limit dengan mensubstitusikan s equals 1.

limit as s rightwards arrow 1 of fraction numerator s cubed minus 1 over denominator s minus 1 end fraction equals fraction numerator 1 cubed minus 1 over denominator 1 minus 1 end fraction equals 0 over 0

Karena hasil penyebutnya 0 maka gunakanlah cara lain untuk mencari limitnya, yaitu dengan pemfaktoran.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as s rightwards arrow 1 of fraction numerator s cubed minus 1 over denominator s minus 1 end fraction end cell equals cell limit as s rightwards arrow 1 of fraction numerator up diagonal strike left parenthesis s minus 1 right parenthesis end strike left parenthesis s squared plus s plus 1 right parenthesis over denominator up diagonal strike s minus 1 end strike end fraction end cell row blank equals cell limit as s rightwards arrow 1 of open parentheses s squared plus s plus 1 close parentheses end cell row blank equals cell 1 squared plus 1 plus 1 end cell row blank equals cell 1 plus 1 plus 1 end cell row blank equals 3 end table

Dengan demikian, nilai limit as s rightwards arrow 1 of fraction numerator s cubed minus 1 over denominator s minus 1 end fraction equals 3.

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