Pertanyaan

N i l ai d a r i x → 2 lim ( t 2 − t − 2 ) 2 ( t 2 − 5 t + 6 ) sin ( t − 2 ) = ...

$N i l ai d a r i x \to 2 lim \frac{( t ^{2} - 5 t + 6 ) sin ( t - 2 )}{( t ^{2} - t - 2 ) ^{2}} = ...$

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Jawaban terverifikasi

Pembahasan

$limit as x rightwards arrow 2 of fraction numerator left parenthesis t squared minus 5 t plus 6 right parenthesis sin left parenthesis t minus 2 right parenthesis over denominator left parenthesis t squared minus t minus 2 right parenthesis squared end fraction equals limit as x rightwards arrow 2 of fraction numerator left parenthesis t squared minus 5 t plus 6 right parenthesis sin left parenthesis t minus 2 right parenthesis over denominator left parenthesis left parenthesis t minus 2 right parenthesis left parenthesis t plus 1 right parenthesis right parenthesis squared end fraction equals limit as x rightwards arrow 2 of fraction numerator left parenthesis t minus 3 right parenthesis left parenthesis t minus 2 right parenthesis sin left parenthesis t minus 2 right parenthesis over denominator left parenthesis t minus 2 right parenthesis squared left parenthesis t plus 1 right parenthesis squared end fraction equals limit as x rightwards arrow 2 of fraction numerator left parenthesis t minus 3 right parenthesis left parenthesis t minus 2 right parenthesis over denominator left parenthesis t minus 2 right parenthesis left parenthesis t plus 1 right parenthesis squared end fraction limit as x rightwards arrow 2 of fraction numerator sin left parenthesis t minus 2 right parenthesis over denominator left parenthesis t minus 2 right parenthesis end fraction equals fraction numerator left parenthesis 2 minus 3 right parenthesis over denominator left parenthesis 2 plus 1 right parenthesis squared end fraction left parenthesis 1 right parenthesis equals negative 1 over 9$