show the correct notation for “The limit of x^2 - 1 as x approaches 3.
do you mean your text has absolutely no discussion of this topic?
Or that using google produces no results?
How about this for such an example?
https://www.mathway.com/popular-problems/Calculus/583678
The correct notation for "The limit of x^2 - 1 as x approaches 3" is written as:
lim(x → 3) (x^2 - 1)
Here's an explanation on how to get the answer:
To find the limit of a function as x approaches a certain value, we substitute that value into the function and see what happens.
In this case, we substitute x = 3 into the function f(x) = x^2 - 1.
So, we evaluate f(3) by plugging in x = 3:
f(3) = (3)^2 - 1 = 9 - 1 = 8
However, to find the limit, we are interested in the behavior of the function as x gets arbitrarily close to 3, but not actually equal to 3.
To find this limit, we substitute values of x that are very close to 3. For example, we can choose x = 3.1, x = 3.01, x = 3.001, and so on.
By evaluating the function for these values of x, we can observe that the result gets closer and closer to 8.
Hence, the limit of (x^2 - 1) as x approaches 3 is:
lim(x → 3) (x^2 - 1) = 8