Pertanyaan

x → a lim x − a cos x − cos a = ...

$x \to a lim \frac{cos x - cos a}{x - a} = ...$

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Jawaban terverifikasi

Pembahasan

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

Ingat kembali sifat-sifat berikut.

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

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.