Tentukan nilai limit berikut
(a) lim
x→3
x
2−5x+6
x2−4x+3
(b) lim
t→−1
t
3−4t
2+t+6
t+1

Mari kita selesaikan kedua limit berikut:

### (a) \(\lim_{x \to 3} \frac{x^2 - 5x + 6}{x^2 - 4x + 3}\)

Langkah-langkah:

1. **Substitusi langsung**:
   Substitusi \(x = 3\) ke dalam fungsi:
   \[
   \frac{3^2 - 5(3) + 6}{3^2 - 4(3) + 3} = \frac{9 - 15 + 6}{9 - 12 + 3} = \frac{0}{0}
   \]
   Hasilnya adalah bentuk tak tentu \( \frac{0}{0} \). Jadi, kita perlu melakukan faktorisasi.

2. **Faktorisasi**:
   - Pembilang: \(x^2 - 5x + 6 = (x - 2)(x - 3)\)
   - Penyebut: \(x^2 - 4x + 3 = (x - 1)(x - 3)\)

   Maka limit menjadi:
   \[
   \lim_{x \to 3} \frac{(x - 2)(x - 3

Tentukan nilai limit berikut (a) lim x→3 (x^2−5x+6)/(x^2−4x+3) (b) lim t→−1 (t^3−4t^2+t+6)/(t+1)

This solution explains how to find the limit of the function (x^2−5x+6)/(x^2−4x+3) as x approaches 3, using factoring techniques for quadratic expressions. It also covers solving limits involving cubic polynomials. Ideal for students in Grades 10-12 learning algebra and limits.

Math Problem Statement

Solution

(a) $\lim_{x \to 3} \frac{x^2 - 5x + 6}{x^2 - 4x + 3}$

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