Step 1: Understand what the limit lim(x→∞) means. It means we want to see what happens to the expression (1/x) as x gets larger and larger, approaching infinity.
Step 2: Consider the expression (1/x). As x increases, the value of x becomes very large.
Step 3: Think about what happens to (1/x) when x is a very large number. For example, if x = 10, (1/x) = 0.1; if x = 100, (1/x) = 0.01; if x = 1000, (1/x) = 0.001.
Step 4: Notice that as x keeps getting larger, (1/x) keeps getting smaller and smaller, getting closer to 0.
Step 5: Conclude that as x approaches infinity, (1/x) approaches 0.
Limits at Infinity – Understanding how functions behave as the variable approaches infinity.
Reciprocal Functions – Analyzing the behavior of the function 1/x as x increases.
