Pertanyaan

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

Hasil dari $x \to 2 lim \frac{x ^{2} - 4 x + 4}{1 - cos ( x - 2 )}$ adalah ....

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

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.