Although your notation is a little ambiguous i am assuming that on A) you meantdenverhockeyfan said:Homework Statement
Use the squeeze theorem to prove the sequence converges to 0. (Givin the lim 1/n=0 and 1/n^2=0.
A) cos n pi / n^2
B) ((-1)^n) ln(n) / n^2
The Squeeze Theorem Problem is a mathematical concept used to determine the limit of a function if it is "squeezed" between two other functions whose limits are known. It is also known as the Sandwich Theorem or the Pinching Theorem.
The Squeeze Theorem works by comparing the limit of a function to the limits of two other functions that are known to be greater than or equal to the original function. If the two functions have the same limit, then the original function will also have the same limit.
The Squeeze Theorem is important in calculus because it provides a method for calculating the limit of a function that may be difficult to solve using other techniques. It is also used to prove the existence of limits and to evaluate indeterminate forms.
For the Squeeze Theorem to be applicable, the three functions being compared must be continuous at the point of interest and the "squeezing" functions must have the same limit as the original function at that point.
Yes, the Squeeze Theorem can be used to evaluate limits at infinity. In this case, the two "squeezing" functions must have limits of infinity or negative infinity, and the original function must be bounded between them.