Question

find the limit of this please
\[\lim_{x \rightarrow -infinity}(5x+12)/\sqrt{9x^2+x-3}\]

Answer 1

\[\lim_{x \rightarrow -\infty}\frac{5x+12}{\sqrt{9x^2+x-3}} \cdot \frac{\frac{1}{\sqrt{x^2}}}{\frac{1}{\sqrt{x^2}}}\]
now recall
\[\sqrt{x^2}=|x|=x \text{ if } x<0 \]
x<0 since we are approaching negative infinity so we have
\[\lim_{x \rightarrow -\infty}\frac{5x+12}{\sqrt{9x^2+x-3}} \cdot \frac{\frac{1}{-x}}{ \frac{1}{\sqrt{x^2}}}\]

Answer 2

\[\lim_{x \rightarrow -\infty} \frac{-5+\frac{-12}{x}}{\sqrt{9+\frac{1}{x}-\frac{3}{x^2}}}\]

Answer 3

\[\frac{-5 +0}{\sqrt{9+0-0}}\]

Answer 4

oops small type-0
|x|=-x if x<0

Answer 5

everything else is good

Answer 6

is the final answer -5/sqrt 9

Answer 7

the sqrt(9)=3

Answer 8

ok i see thanks again myininaya

Answer 9

np