Pertanyaan

Nilai dari x → ∞ lim ( x 2 + 6 x + 8 − x 2 + 2 x )

Nilai dari $x \to \infty lim (x^{2} + 6 x + 8 - x^{2} + 2 x)$

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

Nilai dari adalah 2.

Nilai dari begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of x squared plus 6 x plus 8 end root minus square root of x squared plus 2 x end root close parentheses end style

begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of x squared plus 6 x plus 8 end root minus square root of x squared plus 2 x end root close parentheses end style

adalah 2.

Pembahasan

Ingat! Pada bentuk limit maka . Pada soal nilai , sehingga: Jadi,Nilai dari adalah 2.

Ingat!

Pada bentuk limit begin mathsize 12px style 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 end style maka $begin mathsize 12px style open curly brackets table attributes columnalign left end attributes row cell a less than p rightwards double arrow negative infinity end cell row cell a equals p rightwards double arrow fraction numerator b minus q over denominator 2 square root of a end fraction end cell row cell a greater than p rightwards double arrow infinity end cell end table close end style$ .

Pada soal begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of x squared plus 6 x plus 8 end root minus square root of x squared plus 2 x end root close parentheses end style nilai a equals p , sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of x squared plus 6 x plus 8 end root minus square root of x squared plus 2 x end root close parentheses end cell equals cell fraction numerator 6 minus 2 over denominator 2 square root of 1 end fraction end cell row blank equals cell 4 over 2 end cell row blank equals 2 end table$

Jadi, Nilai dari adalah 2.