The limit as x approaches 0 of the expression 3sin(4x) / sin(3x) can be solved using the fundamental limit lim as x -> 0 of sin(x) / x = 1. By applying the identity sin(2x) = 2sin(x)cos(x) to rewrite sin(4x) as 2sin(2x)cos(2x), the problem simplifies significantly. This manipulation leads to a well-known limit that can be easily evaluated, confirming that the limit exists and can be computed directly.
PREREQUISITESStudents studying calculus, particularly those focusing on limits and trigonometric functions, as well as educators seeking examples for teaching limit evaluation techniques.
