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Pertanyaan

x → a lim ​ x − a cos x − cos a ​ = ...

    

  1.  negative sin space a  

  2.  negative tan space a   

  3. negative cos space a   

  4.  negative 2 space sin space a   

  5. negative 2 space cos space a    

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N. Puspita

Master Teacher

Jawaban terverifikasi

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Pembahasan

Pembahasan
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Ingat kembali sifat-sifat berikut. Dari aturan di atas, maka diperoleh Dengan demikian, . Jadi, jawaban yang benar adalah A.

Ingat kembali sifat-sifat berikut.

  • cos space A minus cos space B equals negative 2 space sin space 1 half left parenthesis A plus B right parenthesis space sin 1 half left parenthesis A minus B right parenthesis      

 

  • limit as x rightwards arrow c of f left parenthesis x right parenthesis times g left parenthesis x right parenthesis equals limit as x rightwards arrow c of f left parenthesis x right parenthesis times limit as x rightwards arrow c of g left parenthesis x right parenthesis

 

  • limit as x rightwards arrow c of fraction numerator sin space a left parenthesis x minus c right parenthesis over denominator b left parenthesis x minus c right parenthesis end fraction equals limit as x rightwards arrow c of fraction numerator space a left parenthesis x minus c right parenthesis over denominator sin space b left parenthesis x minus c right parenthesis end fraction equals a over b 

 

Dari aturan di atas, maka diperoleh

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow a of fraction numerator cos space x minus space cos space a over denominator x minus a end fraction end cell equals cell limit as x rightwards arrow a of fraction numerator negative 2 space sin space begin display style 1 half end style left parenthesis x plus a right parenthesis times sin space begin display style 1 half end style left parenthesis x minus a right parenthesis over denominator x minus a end fraction end cell row blank equals cell limit as x rightwards arrow a of minus 2 space sin space 1 half left parenthesis x plus a right parenthesis times limit as x rightwards arrow a of fraction numerator sin space begin display style 1 half end style left parenthesis x minus a right parenthesis over denominator x minus a end fraction end cell row blank equals cell negative 2 space sin space 1 half left parenthesis a plus a right parenthesis times fraction numerator begin display style 1 half end style over denominator 1 end fraction end cell row blank equals cell negative 2 space sin space 1 half left parenthesis 2 a right parenthesis times 1 half end cell row blank equals cell negative 2 space sin space a times 1 half end cell row blank equals cell negative space sin space a end cell end table end style       

Dengan demikian, limit as x rightwards arrow a of fraction numerator cos space x minus space cos space a over denominator x minus a end fraction equals negative space sin space a.

Jadi, jawaban yang benar adalah A.

 

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Limit Fungsi Trigonometri

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