chaose said:Is there anyway to show that the limit for ((x^2)(sin y)^2)/(x^2+2y^2) exists without using the squeeze theorem? I was thinking about the episilon-delta definition of the limit.
The limit of (x^2)(sin y)^2)/(x^2+2y^2) at (0,0) is equal to 0.
The limit can be proven by using the epsilon-delta definition of a limit and algebraic manipulation.
Proving limits is important in calculus because it allows us to understand the behavior of a function near a specific point, which is crucial in determining the continuity and differentiability of a function.
No, the Squeeze Theorem can only be used to prove limits when the function is "sandwiched" between two other functions whose limits are known.
Yes, besides the Squeeze Theorem, other methods to prove limits include the algebraic limit laws, the epsilon-delta definition, and L'Hopital's rule.