To evaluate the limit:

$\lim_{x \to 4} (x^2 - 4x + 3)$

Step 1: Direct Substitution

Substituting $x = 4$:

$4^2 - 4(4) + 3 = 16 - 16 + 3 = 3$

Conclusion

Since direct substitution gives a finite value, the limit exists and is:

$\lim_{x \to 4} (x^2 - 4x + 3) = 3$

Would you like a more detailed explanation or any additional clarifications?

Related Questions

1. What is the limit of $x^2 - 4x + 3$ as $x \to 3$?
2. How do you find limits algebraically if direct substitution fails?
3. What is the difference between one-sided and two-sided limits?
4. How do you evaluate limits involving indeterminate forms like $0/0$?
5. What role does factorization play in solving limit problems?

Tip: Always check if direct substitution works first when solving limits—it’s the fastest method when applicable.