Nilai dari x→∞lim(3x+1)−9x2−9x+2= ....

Pertanyaan

Nilai dari

$\lim_{x\rightarrow\infty}\left(3x+1\right)-\sqrt{9x^2-9x+2}=$ ....

-2,5
1,5
2,0
2,5
3,0

S. Nur

Master Teacher

Jawaban terverifikasi

Pembahasan

Limit Tak Hingga

Untuk x rightwards arrow infinity dengan hasil infinity minus infinity

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

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses 3 x plus 1 close parentheses minus square root of 9 x squared minus 9 x plus 2 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of open parentheses 3 x plus 1 close parentheses squared end root minus square root of 9 x squared minus 9 x plus 2 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of 9 x squared plus 6 x plus 1 end root minus square root of 9 x squared minus 9 x plus 2 end root end cell row blank equals cell fraction numerator b minus q over denominator 2 square root of a end fraction end cell row blank equals cell fraction numerator 6 minus open parentheses negative 9 close parentheses over denominator 2 square root of 9 end fraction end cell row blank equals cell fraction numerator 6 plus 9 over denominator 2 times 3 end fraction end cell row blank equals cell 15 over 6 end cell row blank equals cell 2 comma 5 end cell end table$

Jadi, nilai dari limit as x rightwards arrow infinity of open parentheses 3 x plus 1 close parentheses minus square root of 9 x squared minus 9 x plus 2 end root equals 2 comma 5 .

Jadi, jawaban yang tepat adalah D.