Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f continuous at x = a. HINT [See Example 2.] (If there is no such value, enter NONE.)
f(x) =
x
2x2 − x
; a = 0
In google type: "function graphs online"
When you see list buf results click on:
rechneronline.de/function-graphs/
When page be open in blue rectacangle type your function and click otion Draw
thanks
To determine the value to assign to f(a) in order to make f continuous at x = a, we can use the concept of a limit.
First, let's analyze the function f(x) = x / (2x^2 - x) for x ≠ 0. We notice that at x = 0, the denominator becomes 0, which results in an undefined value. So, in order to make f continuous at x = a = 0, we need to assign a value to f(0) such that the limit of f(x) as x approaches 0 exists and is equal to f(0).
To find the limit of f(x) as x approaches 0, we can calculate it algebraically.
lim(x->0) (x / (2x^2 - x))
First, factor out x from the denominator:
lim(x->0) (x / (x(2x - 1)))
Next, cancel out the x term:
lim(x->0) (1 / (2x - 1))
Now, substitute 0 into the expression for x:
1 / (2(0) - 1) = -1
Therefore, the limit of f(x) as x approaches 0 is -1.
To make f continuous at x = a = 0, we need f(0) to be equal to the limit we just calculated, which is -1. Hence, we assign f(0) = -1.
Therefore, the value to assign to f(a) to make f continuous at x = a = 0 is f(0) = -1.