Pertanyaan

t → 2 l im ( t − 2 ) ( t 2 + 3 t + 2 ) 4 t 4 + 4 t − 72 = ....

$t \to 2 l im \frac{4 t ^{4} + 4 t - 72}{( t - 2 ) ( t ^{2} + 3 t + 2 )} = ....$

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Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack l i m with t rightwards arrow 2 below fraction numerator 4 t to the power of 4 plus 4 t minus 72 over denominator left parenthesis t minus 2 right parenthesis left parenthesis t squared plus 3 t plus 2 right parenthesis end fraction end cell equals cell stack l i m with t rightwards arrow 2 below fraction numerator left parenthesis t minus 2 right parenthesis left parenthesis 4 t cubed plus 8 t squared plus 16 t plus 32 right parenthesis over denominator left parenthesis t minus 2 right parenthesis left parenthesis t squared plus 3 t plus 2 right parenthesis end fraction end cell row blank equals cell stack l i m with t rightwards arrow 2 below fraction numerator left parenthesis 4 t cubed plus 8 t squared plus 16 t plus 32 right parenthesis over denominator left parenthesis t squared plus 3 t plus 2 right parenthesis end fraction end cell row blank equals cell fraction numerator 4 left parenthesis 2 right parenthesis cubed plus 8 left parenthesis 2 right parenthesis squared plus 16 left parenthesis 2 right parenthesis plus 32 over denominator 2 squared plus 3 left parenthesis 2 right parenthesis plus 2 end fraction end cell row blank equals cell fraction numerator 32 plus 32 plus 32 plus 32 over denominator 4 plus 6 plus 2 end fraction end cell row blank equals cell 128 over 12 end cell row blank equals cell 32 over 3 end cell end table end style$