Find lim x->infinity (x^2-1)/x or state that the limit does not exist.
I'm not good at all with limits.
(x^2 - 1)/x = x - 1/x
so as x becomes large , x - 1/x approaches the value x itself, since 1/x approaches zero.
so limit (x^2-1)/x approaches infinity as x---> infinity
To find the limit as x approaches infinity of the expression (x^2 - 1) / x, you can use a basic trick called algebraic manipulation.
Step 1: Start by dividing each term in the numerator (x^2 - 1) by the highest power of x in the denominator, which is x:
(x^2 / x - 1 / x)
Step 2: Simplify the expression:
(x - 1 / x)
Step 3: Now, as x approaches infinity, the value of 1/x approaches zero. Since the numerator is x, the limit is infinity.
Therefore, the limit as x approaches infinity of (x^2 - 1) / x is infinity.
Keep in mind that this is an example of how to find a limit. In general, you should analyze the behavior of the function to determine if the limit exists or not.