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Nicole M, Maddie B, Jordan, Shelly, Maddie G, Emma, Nora
Sandwich Theorem Part 2
The second part of the sandwich theory doesn't involve a graph, but it's just as easy! Let's go through the steps to find the limit as x approaches 0 of x²cos(1/x²).
1. Isolate the difficult portion of your function.
2. Bound the function and set up an inequality.
3. Tweak the function until it matches your original.
4. Take the limit of each portion.
5. Find your answer!
1. cox(1/x²)
2. All cos functions lie b/w -1 and 1, so -1 ≤ cos(1/x²) ≤ 1.
3. -x² ≤ x²cos(1/x²) ≤ x²
4. 0 ≤ x²cos(1/x²) ≤ 0
5. The limit as x approaches 0 of x²cos(1/x²) is 0!
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