Step 1: Identify the limit we need to find: lim x->0 (sin(3x)/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 3 because we have sin(3x).
Step 4: Apply the limit property: since k = 3, we find that lim x->0 (sin(3x)/x) = 3.
Step 5: Conclude that the limit is 3.
Limit of a Trigonometric Function – This concept involves understanding how to evaluate limits involving trigonometric functions, particularly using the standard limit property of sin(kx)/x as x approaches 0.
