RaySix

Post

at October 31st 2023, 8:13:17 pm.

Question:

Find the limit algebraically as x approaches 3:

\lim_{{x \to 3}} \frac{{x^2 - 9}}{{x - 3}}

Explanation:

To find the limit algebraically, we can simplify the expression by factoring the numerator:

\frac{{(x-3)(x+3)}}{{x-3}}

Next, we can cancel out the common factor of $(x-3)$ :

\frac{{\cancel{(x-3)}(x+3)}}{{\cancel{x-3}}}

After canceling out the common factor, we are left with:

x+3

Finally, we can substitute the value $x=3$ into the simplified expression to find the limit:

\lim_{{x \to 3}} \frac{{x^2 - 9}}{{x - 3}} = \lim_{{x \to 3}} (x+3) = 3+3 = 6

Therefore, the limit of the given expression as $x$ approaches $3$ is $6$ .