I don\'t understand how to find the \"less than or equal to\" and \"greater than
ID: 1887980 • Letter: I
Question
I don't understand how to find the "less than or equal to" and "greater than or equal to" functions for the squeeze theorem.For example, how would you find it in here? (I know the answer, but I don't understand why.)
An= [n*(-1)^(n-1)]/(1+n^2)
NOTE: It would be very helpful to SEE what the Squeeze Theorem process looks like in a problem. I provided an example of a question which I know the answer to, but I do not understand how the process was FULLY done, so it would be very helpful if someone could please explain what is going on, especially how to find the An<Cn<Bn part (those should be "less than/greater than" signs). Thank you.
Explanation / Answer
Understanding The Squeeze Theorem This principle, right here, is known as the squeeze theorem in calculus. Some people call it the sandwich theorem, but I like the term squeeze. Now let's consider the village of Moe, and let's zoom in really close where Eulier and Newton meet up. I can say that the limit, as we approach Moe, of Eulier is this point here. Let's call it the town square. And the limit, as we approach Moe, of Newton is also the town square. Because Eulier is always north of Tiny and Tiny is always north of Newton, I can write that the limit, as we approach Moe, of Tiny is also the town square. So let's make this really formal. If the function g(x) is less than or equal to f(x), which is less than or equal to h(x), and the limit, as we approach some number, of g(x) equals the limit, as we approach that same number, of h(x), then we've squeezed f(x) such that the limit, as we approach the same number, of f(x) is equal to both the limit of both g and h. So in this case, h is like Eulier, g is like Newton and f is like Tiny, and f is squeezed in here. So the limit as we approach Moe is that town square. this sequence is alsways greater than , (-1)^(n-1)/(1 + n*n) or smaller than : n/(1 + n*n)
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