The limit of the function 2x/sin(3x) as x approaches 0 is definitively calculated as 2/3. This conclusion is reached by applying the fundamental limit lim sin(x)/x = 1, which simplifies the expression to lim 2/3 (sin(x)/x) as x approaches 0. The discussion confirms that rewriting the limit as 2/3 (3x)/sin(3x) clarifies the evaluation process, ensuring accuracy in the solution.
PREREQUISITESStudents studying calculus, particularly those focusing on limits and trigonometric functions, as well as educators looking for clear examples of limit evaluations.
domyy said:Homework Statement
lim 2x/(sin3x)
x-> 0
Homework Equations
lim sinx/x = 1
x->0
The Attempt at a Solution
is it correct to say the following:
lim 2/3 (sinx/x)
x-> 0
lim 2/3 (1)
x-> 0
Answer: lim 2x/sin3x = 2/3
x-> 0
Because it's on the book:
cos 2x(2)/3 = 2/3
x->0
So I want to know if I solve it the way I did before, would it be correct?