f(x)=x/x^2 – x find limit???
Pleaseee thnks
...limit as x approaches what value?
lim f(x)
x-->1
&
lim f(x)
x-->0
To find the limit of a function, we need to investigate the behavior of the function as the input approaches a specific value. In this case, we want to find the limit of the function f(x) = x / (x^2 - x) as x approaches a certain value.
To begin, let's first factor out x from the denominator using the distributive property:
f(x) = x / (x * (x - 1))
Now we can see that x appears both in the numerator and the denominator. We can simplify further by canceling out the x's:
f(x) = 1 / (x - 1)
Now, we can analyze the limit of the function as x approaches a particular value, let's say "a." We express this as:
lim(x->a) f(x)
Substituting our simplified expression for f(x):
lim(x->a) (1 / (x - 1))
To evaluate this limit, we need to consider the behavior of (x - 1) as x approaches a. If (x - 1) approaches zero, then the denominator will become zero, and the limit will not exist.
Let's examine this situation:
If (x - 1) approaches zero, then we have:
lim(x->a) (1 / (x - 1)) = 1 / (0)
Since the denominator becomes zero, the limit is undefined in this case. Thus, the limit of the function f(x) = x / (x^2 - x) as x approaches a certain value does not exist.