dirk_mec1 said:What happens if you look at y=sqrt(x)?
The Squeeze Theorem, also known as the Sandwich Theorem, is a powerful tool in Multivariable Calculus that is used to evaluate limits. It states that if two functions, f(x) and g(x), are both approaching the same limit as x approaches a certain value, and if there is a third function, h(x), that is always between f(x) and g(x) near that value, then h(x) will also approach the same limit.
The Squeeze Theorem should be used when a limit cannot be evaluated directly, either because the function is undefined at that point or the limit results in an indeterminate form such as 0/0 or ∞/∞. In these cases, the Squeeze Theorem can help to prove the existence of the limit and determine its value.
To use the Squeeze Theorem, you first need to identify the functions f(x), g(x), and h(x) that are involved in the limit. Then, you need to show that h(x) is always between f(x) and g(x) near the value that x is approaching. Finally, you can evaluate the limit by plugging in the limit value to h(x) and using the limits of f(x) and g(x) to determine the limit of h(x).
No, the Squeeze Theorem can only be used for limits involving real numbers. It cannot be used for limits involving complex numbers, as the concept of "squeezing" does not apply in the complex plane.
Yes, the Squeeze Theorem can only be used when the limit of h(x) can be easily determined. If the limit of h(x) is also an indeterminate form, then the Squeeze Theorem cannot be used. Additionally, the Squeeze Theorem can only be used when the functions involved are continuous near the value that x is approaching.