Final answer:
Using a calculator, graphical analysis can indicate if a limit exists, yet analytical techniques like L'Hôpital's Rule, algebraic simplification, or rationalization provide a more precise means to determine limits. These methods avoid the potential inaccuracies of graphical interpretation due to screen or scale limitations.
Step-by-step explanation:
To determine if a limit exists using a calculator, one of the options mentioned is B) Graphical analysis. While this can be done visually by looking at the graph of the function and seeing if the function approaches a certain value from both the left and the right as x approaches a point, analytical techniques are potentially more accurate. For example, options A) L'Hôpital's Rule, C) Algebraic simplification, and D) Rationalization involve precise mathematical procedures that can help in confirming the existence and value of a limit. These analytical methods provide a more exact approach as they involve direct computation rather than visual interpretation which can sometimes be imprecise due to the limitations of a calculator's screen resolution or a graph's scale.
When using analytical techniques, it is important to:
- Eliminate terms wherever possible to simplify the algebra.
- Check the answer to see if it is reasonable.