Step 1: Identify the limit we want to find: lim (x -> 0) (sin(5x)/x).
Step 2: Recognize that this limit can be solved using a known limit property: lim (x -> 0) (sin(kx)/x) = k, where k is a constant.
Step 3: In our case, k is 5 because we have sin(5x).
Step 4: Apply the limit property: since k = 5, we find that lim (x -> 0) (sin(5x)/x) = 5.
Step 5: Conclude that the limit is 5.
Limit of a Function – Understanding how to evaluate limits, particularly those involving trigonometric functions and their behavior as they approach zero.
Sine Limit Property – Applying the specific limit property that states lim (x -> 0) (sin(kx)/x) = k, which is crucial for solving this type of limit problem.
