The limit of (1-cos(2x^2)) / (1-cos(3x^2)) as x approaches 0 results in an indeterminate form of 0/0. The discussion highlights the use of l'Hôpital's Rule, which initially leads to another 0/0 form. A more effective approach involves recognizing the limit property of sin(x)/x as x approaches 0, specifically that lim (x→0) sin(x)/x = 1. This insight allows for a more straightforward resolution of the limit without repeated application of l'Hôpital's Rule.
PREREQUISITESStudents studying calculus, particularly those focusing on limits and indeterminate forms, as well as educators seeking effective teaching strategies for limit evaluation techniques.
kira137 said:Homework Statement
Find
limit ...(1-cos(2x^2)) / (1-cos(3x^2))
x->0
2. The attempt at a solution
since the above gave me 0/0, I used l'Hopital method..
then i got
(4x)sin(2x^2) / (6x)(sin3x^2)
which gives me 0/0 again..
so I kept on using l'Hopital..