Pertanyaan

Tentukan nilai x → ∞ lim 4 x 2 + 2 x − 2 − 4 x 2 + 3 x − 8 = ...

Tentukan nilai $x \to \infty lim 4 x^{2} + 2 x - 2 - 4 x^{2} + 3 x - 8 = ...$

N. Puspita

Master Teacher

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Jawaban

nilai

limit as x rightwards arrow infinity of space square root of 4 x squared plus 2 x minus 2 end root minus square root of 4 x squared plus 3 x minus 8 end root equals negative 1 fourth

Pembahasan

Jika , maka jika dan hanya jika jika dan hanya jika jika dan hanya jika Pada , nilai sehingga Dengan demikian, nilai

Jika limit as x rightwards arrow infinity of space square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root equals L , maka

L equals negative infinity jika dan hanya jika a less than p

$L equals fraction numerator b minus q over denominator 2 square root of a end fraction$ jika dan hanya jika a equals p

L equals infinity jika dan hanya jika a greater than p

Pada limit as x rightwards arrow infinity of space square root of 4 x squared plus 2 x minus 2 end root minus square root of 4 x squared plus 3 x minus 8 end root , nilai a equals p sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row L equals cell fraction numerator b minus q over denominator 2 square root of a end fraction end cell row blank equals cell fraction numerator 2 minus 3 over denominator 2 square root of 4 end fraction end cell row blank equals cell negative fraction numerator 1 over denominator 2 times 2 end fraction end cell row blank equals cell negative 1 fourth end cell end table$

Dengan demikian, nilai limit as x rightwards arrow infinity of space square root of 4 x squared plus 2 x minus 2 end root minus square root of 4 x squared plus 3 x minus 8 end root equals negative 1 fourth

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