Pertanyaan

Nilai dari x → 0 lim ( x 2 − 2 x + 1 − x 2 + 3 x − 4 ) adalah ...

Nilai dari $x \to 0 lim (x^{2} - 2 x + 1 - x^{2} + 3 x - 4)$ adalah ...

N. Puspita

Master Teacher

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Pembahasan

Terdapat kesalahan pada soal. Bukan , melainkan . Ingat! Diketahui , maka: Sehingga, nilai dari limit tersebut adalah: Sehingga, . Jadi, tidak ada jawaban yang tepat.

Terdapat kesalahan pada soal. Bukan limit as x rightwards arrow 0 of open parentheses square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x minus 4 end root close parentheses , melainkan limit as x rightwards arrow infinity of open parentheses square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x minus 4 end root close parentheses .

Ingat!

$limit as x rightwards arrow infinity of open parentheses square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root close parentheses equals open curly brackets table attributes columnalign left end attributes row cell infinity comma space untuk space a greater than p end cell row cell table row cell fraction numerator b minus q over denominator 2 square root of a end fraction comma space untuk space a equals p end cell row cell negative infinity comma space untuk space a less than p end cell end table end cell end table close$

Diketahui limit as x rightwards arrow infinity of open parentheses square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x minus 4 end root close parentheses , maka:

table attributes columnalign right center left columnspacing 0px end attributes row a equals cell 1 comma space b equals negative 2 comma space c equals 1 end cell row p equals cell 1 comma space q equals 3 comma space r equals negative 4 end cell end table

Sehingga, nilai dari limit tersebut adalah:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses square root of x squared minus 2 x plus 1 end root minus square root of x squared plus 3 x minus 4 end root close parentheses end cell row blank equals cell fraction numerator b minus q over denominator 2 square root of a end fraction end cell row blank equals cell fraction numerator negative 2 minus 3 over denominator 2 square root of 1 end fraction end cell row blank equals cell fraction numerator negative 5 over denominator 2 end fraction end cell row blank equals cell negative 2 1 half end cell end table$

Sehingga, .

Jadi, tidak ada jawaban yang tepat.