Pertanyaan

Nilai dari x → 1 lim tan 2 ( 2 x − 2 ) ( x 2 − 1 ) sin ( 3 x − 3 ) adalah ...

Nilai dari $x \to 1 lim \frac{( x ^{2} - 1 ) sin ( 3 x - 3 )}{tan ^{2} ( 2 x - 2 )}$ adalah ...

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Klaim

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

Jika pada limit dilakukan substitusi langsung akan menghasilkan , sehingga pada bentuk pecahan perlu diuraikan dan disederhanakan sebagai berikut:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of space fraction numerator open parentheses x squared minus 1 close parentheses space. space sin open parentheses 3 x minus 3 close parentheses over denominator tan squared open parentheses 2 x minus 2 close parentheses end fraction space end cell row blank equals cell space limit as x rightwards arrow 1 of space fraction numerator open parentheses x minus 1 close parentheses space open parentheses x plus 1 close parentheses. space sin 3 open parentheses x minus 1 close parentheses over denominator tan open parentheses 2 x minus 2 close parentheses space tan open parentheses 2 x minus 2 close parentheses end fraction end cell row blank equals cell space space limit as x rightwards arrow 1 of space fraction numerator open parentheses x minus 1 close parentheses space open parentheses x plus 1 close parentheses. space sin 3 open parentheses x minus 1 close parentheses over denominator tan space 2 open parentheses x minus 1 close parentheses space tan space 2 open parentheses x minus 1 close parentheses end fraction end cell row blank equals cell space limit as x rightwards arrow 1 of space open parentheses x plus 1 close parentheses space fraction numerator open parentheses x minus 1 close parentheses over denominator tan space 2 open parentheses x minus 1 close parentheses end fraction space. space fraction numerator sin 3 open parentheses x minus 1 close parentheses over denominator tan 2 open parentheses x minus 1 close parentheses end fraction end cell row blank equals cell space limit as x rightwards arrow 1 of space left parenthesis x plus 1 right parenthesis space 1 half space 3 over 2 end cell row blank equals cell space 2. space 1 half space. space 3 over 2 space end cell row blank equals cell space 3 over 2 end cell end table$