if f(x)is
greater or equal to 10x–42 but less than or equal to x2+2x–26
determine limx4f(x) =
What theorem did you use to arrive at your answer?
I would like to know what limx4f(x) means.
as lim goes to 4
i got -2
but i don't know what the theorem is called
http://en.wikipedia.org/wiki/Squeeze_theorem
Not all will call this a theorem, many call it a principle.
To find the limit of a function, we need to evaluate the function as x approaches a specific value. In this case, we are given a function f(x) that lies between two other functions, and we need to find the limit as x approaches 4.
First, let's simplify the inequality f(x) ≥ 10x – 42 and f(x) ≤ x^2 + 2x – 26.
For f(x) ≥ 10x – 42, we can rewrite the equation as f(x) – 10x + 42 ≥ 0.
Similarly, for f(x) ≤ x^2 + 2x – 26, we can rewrite the equation as -f(x) + x^2 + 2x – 26 ≥ 0.
Now, we can define a new function g(x) = f(x) – x^2 – 12.
For g(x) to be greater than or equal to 0, we have g(x) ≥ 0.
Therefore, we have:
g(x) = f(x) – x^2 – 12 ≥ 0.
Now, let's find the limit as x approaches 4 for the function g(x).
limx→4 g(x) = g(4).
To evaluate g(4), substitute x = 4 into the equation:
g(4) = f(4) – 4^2 – 12.
Now, we need the value of f(4) to be able to compute g(4).
Unfortunately, without more information about the function f(x) or specific values of x, it is not possible to determine the exact value of limx→4 f(x) or the theorem that was used.