19. [-1t Points] DETALS MY NOTES SCALCETY 2XP2OTL. ASK FOUR Use a tablie of values the estimate the value of the limit. If you have a graphing ctevics, use it un anmimn your tesut graghicail. (Round your answer to bwo decimal places.) \[ \lim _{x \rightarrow \infty} \frac{\sqrt{x+36}-6}{x} \] \( \square \) Need Help? Beodit Wamel t

To estimate the limit \(\lim _{x \rightarrow \infty} \frac{\sqrt{x+36}-6}{x}\) using a table of values, pick large values of \(x\) such as 100, 1000, and 10,000. As you compute, you'll find that the expression approaches zero. The pattern indicates that as \(x\) increases, the limit will get closer to 0. For a more visual approach, you can graph the function \(\frac{\sqrt{x+36}-6}{x}\) on graphing software. As you observe the graph while extending \(x\) towards infinity, you'll see the curve quickly approaches the x-axis, further confirming that the limit converges to 0, providing a great visual representation of what happens at infinity!