- #1
bezgin
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How can we prove that the lim (x->1) x^2 + 2 is NOT equal to 2.999? (example I made up right now) At the end of each proof we find a relation between epsilon and delta. What does it mean?
To prove this, we can use the epsilon-delta definition of a limit. We need to show that for any epsilon greater than 0, there exists a delta greater than 0 such that for all x values within a distance of delta from 1, the function x^2 + 2 does not equal 2.999.
The value of the limit is 3. This can be seen by plugging in x=1 into the function x^2 + 2, which gives us a value of 3.
While the graph may give us a visual understanding of the function, it is not a formal proof. We need to use the epsilon-delta definition to prove the limit.
The value 2.999 is the approximation of the limit of (x->1) x^2 + 2. It is not the exact value, and we need to prove that it is not equal to the limit of 3.
No, it is not possible for the limit to equal 2.999 because the function is continuous and the limit of a continuous function is equal to the value of the function at that point, which is 3 in this case. Therefore, the limit cannot be equal to any other value, including 2.999.