The given expression is a limit problem in calculus. Here's how you can solve it:

1. First, simplify the expression inside the limit. The expression is (x^2 - 9) / (x^2 - 4x + 3).

2. Factorize the numerator and the denominator. The numerator x^2 - 9 can be factorized into (x - 3)(x + 3), and the denominator x^2 - 4x + 3 can be factorized into (x - 1)(x - 3).

3. So, the expression becomes lim (x→3) [(x - 3)(x + 3)] / [(x - 1)(x - 3)].

4. Now, cancel out the common factors in the numerator and the denominator. The common factor is (x - 3). So, the expression becomes lim (x→3) (x + 3) / (x - 1).

5. Now, substitute x = 3 into the simplified expression. The expression becomes (3 + 3) / (3 - 1) = 6 / 2 = 3.

So, the value of the limit as x approaches 3 is 3.

Question

The given expression is a limit problem in calculus. Here's how you can solve it:

1. First, simplify the expression inside the limit. The expression is (x^2 - 9) / (x^2 - 4x + 3).

2. Factorize the numerator and the denominator. The numerator x^2 - 9 can be factorized into (x - 3)(x + 3), and the denominator x^2 - 4x + 3 can be factorized into (x - 1)(x - 3).

3. So, the expression becomes lim (x→3) [(x - 3)(x + 3)] / [(x - 1)(x - 3)].

4. Now, cancel out the common factors in the numerator and the denominator. The common factor is (x - 3). So, the expression becomes lim (x→3) (x + 3) / (x - 1).

5. Now, substitute x = 3 into the simplified expression. The expression becomes (3 + 3) / (3 - 1) = 6 / 2 = 3.

So, the value of the limit as x approaches 3 is 3.

Knowee AI · Accepted Answer

The given expression is a limit problem in calculus. Here's how you can solve it:

1. First, simplify the expression inside the limit. The expression is (x^2 - 9) / (x^2 - 4x + 3).

2. Factorize the numerator and the denominator. The numerator x^2 - 9 can be factorized into (x - 3)(x + 3), and the denominator x^2 - 4x + 3 can be factorized into (x - 1)(x - 3).

3. So, the expression becomes lim (x→3) [(x - 3)(x + 3)] / [(x - 1)(x - 3)].

4. Now, cancel out the common factors in the numerator and the denominator. The common factor is (x - 3). So, the expression becomes lim (x→3) (x + 3) / (x - 1).

5. Now, substitute x = 3 into the simplified expression. The expression becomes (3 + 3) / (3 - 1) = 6 / 2 = 3.

So, the value of the limit as x approaches 3 is 3.

he value of lim𝑥→3𝑥2−9𝑥2−4𝑥+3 is __________(rounded off to the nearest integer).

Question

The value of $\lim_{x \to 3} \frac{x^2 - 9}{x^2 - 4x + 3}$ is __________ (rounded off to the nearest integer).

Solution

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