Question

homework 1.2: limits involving infinity score: 27/36 answered: 16/18 progress saved done √0 question 17 0/2 pts 8 49 details evaluate the limit. hint: factor expressions on the top and on the bottom and simplify the fraction. lim (x³ - x)/(x² - 1) as x→1

Explanation:

Step1: Factor the numerator and denominator

The numerator $x^{3}-x=x(x^{2} - 1)=x(x - 1)(x + 1)$ and the denominator $x^{2}-1=(x - 1)(x + 1)$.
So the function becomes $\frac{x(x - 1)(x + 1)}{(x - 1)(x + 1)}$.

Step2: Simplify the fraction

Cancel out the common factors $(x - 1)$ and $(x + 1)$ (for $x
eq1$ and $x
eq - 1$). The simplified function is $y = x$.

Step3: Evaluate the limit

Now, find $\lim_{x
ightarrow1}x$. Substitute $x = 1$ into $y=x$.
$\lim_{x
ightarrow1}x=1$.

Answer:

$1$