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Hasil dari begin mathsize 14px style limit as x rightwards arrow 1 of invisible function application fraction numerator tan invisible function application open parentheses x squared plus 4 x minus 5 close parentheses over denominator sin invisible function application open parentheses x squared minus 1 close parentheses end fraction end style  adalah ....

  1. begin mathsize 14px style 6 end style 

  2. begin mathsize 14px style 3 end style 

  3. begin mathsize 14px style 1 end style 

  4. begin mathsize 14px style negative 3 end style 

  5. begin mathsize 14px style negative 6 end style 

M. Robo

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Perhatikan bahwa

begin mathsize 14px style limit as x rightwards arrow 1 of invisible function application fraction numerator tan invisible function application open parentheses x squared plus 4 x minus 5 close parentheses over denominator sin invisible function application open parentheses x squared minus 1 close parentheses end fractionequals limit as x rightwards arrow 1 of invisible function application fraction numerator tan invisible function application open parentheses open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses close parentheses over denominator sin invisible function application open parentheses open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses close parentheses end fractionequals limit as x rightwards arrow 1 of invisible function application open parentheses fraction numerator tan invisible function application open parentheses open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses close parentheses over denominator sin invisible function application open parentheses open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses close parentheses end fraction times fraction numerator open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses end fraction times fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses over denominator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses end fraction close parenthesesequals limit as x rightwards arrow 1 of invisible function application open parentheses fraction numerator tan invisible function application open parentheses open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses end fraction times fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses over denominator sin invisible function application open parentheses open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses close parentheses end fraction times fraction numerator open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses over denominator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses end fraction close parenthesesequals limit as x rightwards arrow 1 of invisible function application fraction numerator tan invisible function application open parentheses open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses end fraction times limit as x rightwards arrow 1 of invisible function application fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses over denominator sin invisible function application open parentheses open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses close parentheses end fraction times limit as x rightwards arrow 1 of invisible function application fraction numerator open parentheses x plus 5 close parentheses up diagonal strike open parentheses x minus 1 close parentheses end strike over denominator open parentheses x plus 1 close parentheses up diagonal strike open parentheses x minus 1 close parentheses end strike end fractionequals limit as x rightwards arrow 1 of invisible function application fraction numerator tan invisible function application open parentheses open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses end fraction times limit as x rightwards arrow 1 of invisible function application fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses over denominator sin invisible function application open parentheses open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses close parentheses end fraction times limit as x rightwards arrow 1 of invisible function application fraction numerator open parentheses x plus 5 close parentheses over denominator open parentheses x plus 1 close parentheses end fraction end style   

Karena begin mathsize 14px style x rightwards arrow 1 end style, maka begin mathsize 14px style open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses rightwards arrow 0 end style dan begin mathsize 14px style open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses rightwards arrow 0 end style.

Oleh karena itu,

begin mathsize 14px style limit as x rightwards arrow 1 of invisible function application fraction numerator tan invisible function application open parentheses open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses end fraction equals limit as open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses rightwards arrow 0 of invisible function application fraction numerator tan invisible function application open parentheses open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses end fraction equals 1limit as x rightwards arrow 1 of invisible function application fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses over denominator sin invisible function application open parentheses open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses close parentheses end fraction equals limit as open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses rightwards arrow 0 of invisible function application fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses over denominator sin invisible function application open parentheses open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses close parentheses end fraction equals 1 end style                   

Kemudian, didapat

begin mathsize 14px style limit as x rightwards arrow 1 of invisible function application fraction numerator tan invisible function application open parentheses x squared plus 4 x minus 5 close parentheses over denominator sin invisible function application open parentheses x squared minus 1 close parentheses end fractionequals limit as x rightwards arrow 1 of invisible function application fraction numerator tan invisible function application open parentheses open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses end fraction times limit as x rightwards arrow 1 of invisible function application fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses over denominator sin invisible function application open parentheses open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses close parentheses end fraction times limit as x rightwards arrow 1 of invisible function application fraction numerator open parentheses x plus 5 close parentheses over denominator open parentheses x plus 1 close parentheses end fractionequals 1 times 1 times fraction numerator open parentheses 1 plus 5 close parentheses over denominator open parentheses 1 plus 1 close parentheses end fractionequals 6 over 2equals 3 end style   

Jadi, jawaban yang tepat adalah B.

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