When it comes to determining limits, graphical methods can provide valuable insights. Graphs help visualize the behavior of functions and can assist in finding limits through visual analysis.

One way to use graphical methods is to observe the behavior of a function as it approaches a particular value. If the function approaches a single fixed value, then that value is the limit. For example, consider the function f(x) = 2x + 3. As x approaches 2, we can see from the graph that the function approaches the value 7. Therefore, the limit as x approaches 2 is 7.

Another graphical approach involves using the intermediate value theorem to determine continuity. This theorem states that if a function is continuous on the closed interval [a, b], then it takes on all values between f(a) and f(b). By examining the graph, we can determine whether the function is continuous or exhibits discontinuities within the given interval.

Lastly, graphs can help identify vertical and horizontal asymptotes. A vertical asymptote occurs when the function approaches infinity or negative infinity as x tends to a particular value. A horizontal asymptote, on the other hand, is a horizontal line which the function approaches as x tends to positive or negative infinity.

With graphical methods, determining limits becomes more intuitive and easier to grasp. So keep practicing, and soon you'll be a master at using graphs to find limits!