Pertanyaan

lim t → − 8 t + 8 t 2 − 64 = ...

$lim_{t \to - 8} \frac{t ^{2} - 64}{t + 8} = ...$

J. Joko

Master Teacher

Jawaban terverifikasi

Jawaban

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$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as t rightwards arrow negative 8 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator t squared minus 64 over denominator t plus 8 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 16 end table end style$ .

Pembahasan

Substitusi Karena didapat bentuk yang merupakan bentuk tak tentu, maka difaktorkan dahulu. Jadi, .

Substitusi

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as t rightwards arrow negative 8 of fraction numerator t squared minus 64 over denominator t plus 8 end fraction end cell row blank equals cell fraction numerator left parenthesis negative 8 right parenthesis squared minus 64 over denominator left parenthesis negative 8 right parenthesis plus 8 end fraction end cell row blank equals cell 0 over 0 end cell row blank blank blank end table end style$

Karena didapat bentuk yang merupakan bentuk tak tentu, maka difaktorkan dahulu.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as t rightwards arrow negative 8 of fraction numerator t squared minus 64 over denominator t plus 8 end fraction end cell row blank equals cell limit as t rightwards arrow negative 8 of fraction numerator left parenthesis t plus 8 right parenthesis left parenthesis t minus 8 right parenthesis over denominator t plus 8 end fraction end cell row blank equals cell limit as t rightwards arrow negative 8 of left parenthesis t minus 8 right parenthesis end cell row blank equals cell negative 8 minus 8 end cell row blank equals cell negative 16 end cell end table end style$

Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as t rightwards arrow negative 8 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator t squared minus 64 over denominator t plus 8 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 16 end table end style$ .