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Jika diketahui begin mathsize 14px style limit as x rightwards arrow 0 of invisible function application fraction numerator a x tan invisible function application x minus b over denominator cos invisible function application 5 x minus cos invisible function application 3 x end fraction equals 5 end style, maka nilai begin mathsize 14px style a minus b end style adalah ....

  1. begin mathsize 14px style negative 40 end style 

  2. begin mathsize 14px style negative 8 end style 

  3. begin mathsize 14px style negative 5 end style 

  4. begin mathsize 14px style 8 end style 

  5. begin mathsize 14px style 40 end style 

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A. space space 

Pembahasan

Perhatikan bahwa jika x disubstitusi dengan 0, didapat bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of invisible function application fraction numerator a x tan invisible function application x minus b over denominator cos invisible function application 5 x minus cos invisible function application 3 x end fraction end cell equals 5 row cell fraction numerator a times 0 times tan invisible function application 0 minus b over denominator cos invisible function application open parentheses 5 times 0 close parentheses minus cos invisible function application open parentheses 3 times 0 close parentheses end fraction end cell equals 5 row cell fraction numerator negative b over denominator 1 minus 1 end fraction end cell equals 5 end table end style               

Perhatikan bahwa pada bagian penyebut didapat begin mathsize 14px style 1 minus 1 equals 0 end style.

Karena limit tersebut memiliki hasil, haruslah pembilang juga bernilai 0, sehingga dimiliki bentuk tak tentu size 14px 0 over size 14px 0.     

Oleh karena itu,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative b end cell equals 0 row b equals 0 end table end style

Ingat bahwa

begin mathsize 14px style cos invisible function application alpha minus cos invisible function application beta equals negative 2 sin invisible function application open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses sin invisible function application open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses end style           

Oleh karena itu, didapat

undefined             

Kemudian, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of invisible function application fraction numerator a x tan invisible function application x minus b over denominator cos invisible function application 5 x minus cos invisible function application 3 x end fraction end cell equals 5 row cell limit as x rightwards arrow 0 of invisible function application fraction numerator a x tan invisible function application x minus 0 over denominator negative 2 sin invisible function application 4 x sin invisible function application x end fraction end cell equals 5 row cell limit as x rightwards arrow 0 of invisible function application fraction numerator a x tan invisible function application x over denominator negative 2 sin invisible function application 4 x sin invisible function application x end fraction end cell equals 5 row cell limit as x rightwards arrow 0 of invisible function application fraction numerator a x over denominator negative 2 sin invisible function application 4 x end fraction times limit as x rightwards arrow 0 of invisible function application fraction numerator tan invisible function application x over denominator sin invisible function application x end fraction end cell equals 5 row cell limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator a x over denominator negative 2 sin invisible function application 4 x end fraction times 4 over 4 close parentheses times limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator tan invisible function application x over denominator sin invisible function application x end fraction times x over x close parentheses end cell equals 5 row cell limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator 4 x over denominator sin invisible function application 4 x end fraction times fraction numerator a over denominator negative 2 times 4 end fraction close parentheses times limit as x rightwards arrow 0 of invisible function application open parentheses fraction numerator tan invisible function application x over denominator x end fraction times fraction numerator x over denominator sin invisible function application x end fraction close parentheses end cell equals 5 row cell open parentheses 1 times fraction numerator a over denominator negative 8 end fraction close parentheses times open parentheses 1 times 1 close parentheses end cell equals 5 row cell negative a over 8 end cell equals 5 row a equals cell negative 40 end cell end table end style                   

Oleh karena itu, didapat

begin mathsize 14px style a minus b equals negative 40 minus 0 equals negative 40 end style 

Jadi, jawaban yang tepat adalah A. space space 

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