Pertanyaan

Hasil dari x → 2 lim ​ 1 − cos ( x − 2 ) x 2 − 4 x + 4 ​ adalah ....

Hasil dari  adalah ....

  1. begin mathsize 14px style 1 fourth end style 

  2. undefined 

  3. begin mathsize 14px style 1 end style 

  4. begin mathsize 14px style 2 end style 

  5. begin mathsize 14px style 4 end style 

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa sehingga Jadi, jawaban yang tepat adalah D.

Perhatikan bahwa

begin mathsize 14px style c o s space alpha equals 1 minus 2 s i n squared space 1 half alpha end style  

sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x squared minus 4 x plus 4 over denominator 1 minus cos open parentheses x minus 2 close parentheses end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x minus 2 close parentheses squared over denominator 1 minus open parentheses 1 minus 2 space sin squared begin display style 1 half end style open parentheses x minus 2 close parentheses close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x minus 2 close parentheses squared over denominator 2 space sin squared open parentheses begin display style fraction numerator x minus 2 over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x minus 2 close parentheses open parentheses x minus 2 close parentheses over denominator 2 space sin open parentheses begin display style fraction numerator x minus 2 over denominator 2 end fraction end style close parentheses space sin open parentheses begin display style fraction numerator x minus 2 over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator 2 space sin open parentheses begin display style fraction numerator x minus 2 over denominator 2 end fraction end style close parentheses end fraction times limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator sin open parentheses begin display style fraction numerator x minus 2 over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator begin display style fraction numerator x minus 2 over denominator 2 end fraction end style over denominator sin open parentheses begin display style fraction numerator x minus 2 over denominator 2 end fraction end style close parentheses end fraction times limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator sin open parentheses begin display style fraction numerator x minus 2 over denominator 2 end fraction end style close parentheses end fraction times 2 over 2 end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator begin display style fraction numerator x minus 2 over denominator 2 end fraction end style over denominator sin open parentheses begin display style fraction numerator x minus 2 over denominator 2 end fraction end style close parentheses end fraction times limit as x rightwards arrow 2 of fraction numerator begin display style fraction numerator x minus 2 over denominator 2 end fraction end style over denominator sin open parentheses begin display style fraction numerator x minus 2 over denominator 2 end fraction end style close parentheses end fraction times 2 end cell row blank equals cell 1 times 1 times 2 end cell row blank equals 2 end table end style 

Jadi, jawaban yang tepat adalah D.

144

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Hasil dari x → 0 lim ​ sin 3 x cos 9 x − sin 3 x cos 3 x sin 6 x − tan 6 x ​ adalah ....

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