Question

limit of (5x+2)/sqrt(9x^2+3x+1)-x as x approaches -infinity

Answer 1

\[\text{Limit}\left[\frac{5 x+2}{\sqrt{9 x^2+3 x+1}-x},x\to \text{Infinity}\right]=\frac{5}{2} \]

Answer 2

rob its approaching negative infinity

Answer 3

also can you please demonstrate in steps. i need to understand how to to dow this. and the denominator is actually sqrt(9x^2+x-3) sorry

Answer 4

crap let me rewrite the question... i made alot of mistakes

Answer 5

\[\lim_{x \rightarrow -infinity}(5x+12)/\sqrt{9x^2+x-3}\]

Answer 6

Sorry. missed the -infinity requirement.\[\text{Limit}\left[\frac{5 x+2}{\sqrt{9 x^2+ x-3}},x\to -\text{Infinity}\right]=-\frac{5}{3}=1.6667 \]A plot of the problem expression from -100 throught zero is attached.

Cannot help you on the solution process. Using Mathematica for the answers and plot generation.

Answer 7

ok this is the last one, do you think you can help me
\[\lim_{x \rightarrow infinity}\sqrt{x^2+3x+1}-x\]

Answer 8

I'll try

Answer 9

\[\text{Limit}\left[\sqrt{x^2+3 x+1}-x,x\to \text{Infinity}\right]=\frac{3}{2}=1.5 \]Refer to the attached plot.