Pertanyaan

Nilai dari x → ∞ lim 4 x 2 + 8 − x 2 + 1 − x 2 + x = ...

Nilai dari $x \to \infty lim 4 x^{2} + 8 - x^{2} + 1 - x^{2} + x = ...$

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Jawaban terverifikasi

Pembahasan

Ingat kembali rumus limit berikut : Maka: Penyelesaian bagian pertama : Penyelesaian bagian kedua : Penyelesaian bagian ketiga :

Ingat kembali rumus limit berikut :

$limit as x rightwards arrow infinity of open parentheses square root of a x squared plus b x plus c end root space minus square root of p x squared plus q x plus r end root close parentheses equals fraction numerator left parenthesis b minus q right parenthesis over denominator left parenthesis 2 square root of a right parenthesis end fraction$

Maka:

Penyelesaian bagian pertama :

$limit as x rightwards arrow infinity of left parenthesis square root of 4 x squared plus 8 x end root minus square root of 2 x squared end root right parenthesis equals limit as x rightwards arrow infinity of left parenthesis square root of 4 x squared plus 8 x end root minus square root of 4 x squared end root equals fraction numerator 8 minus 0 over denominator 2 square root of 4 end fraction equals 8 over 4 equals 2$

Penyelesaian bagian kedua :

$limit as x rightwards arrow infinity of square root of x squared end root minus square root of x squared plus 1 end root equals fraction numerator 0 minus 0 over denominator 2 square root of 1 end fraction space equals 0$

Penyelesaian bagian ketiga :

$limit as x rightwards arrow infinity of left parenthesis square root of x squared end root minus square root of x squared plus 3 x end root equals fraction numerator 0 minus 3 over denominator 2 square root of 1 end fraction space right parenthesis equals negative 3 over 2 J a d i comma space limit as x rightwards arrow infinity of space left parenthesis square root of 4 x squared plus 8 x end root minus 2 x plus x minus square root of x squared plus 1 end root plus x minus square root of x squared plus 3 x end root equals 2 plus 0 plus left parenthesis fraction numerator negative 3 over denominator 2 end fraction right parenthesis equals 1 half$