lim _(x arrow 3) f(x)=(x^3-3 x^2-2 x+6)/(x-3)

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Pertanyaan

lim _(x arrow 3) f(x)=(x^3-3 x^2-2 x+6)/(x-3)

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Answer 1

To find the limit of the given function as \( x \) approaches 3, we can try to simplify the expression. Let's factor the numerator:

\[ x^3 - 3x^2 - 2x + 6 \]

We can use polynomial division or synthetic division to divide by \( x - 3 \). Let's use synthetic division:

```
3 | 1 -3 -2 6
| 3 0 -6
----------------
1 0 -2 0
```

The quotient is \( x^2 + 0x - 2 \), so we can rewrite the function as:

\[ f(x) = \frac{x^3 - 3x^2 - 2x + 6}{x - 3} = x^2 - 2 \]

Now, we can find the limit as \( x \) approaches 3:

\[ \lim_{x \to 3} f(x) = \lim_{x \to 3} (x^2 - 2) = 3^2 - 2 = 9 - 2 = 7 \]

Therefore, the limit of the given function as \( x \) approaches 3 is 7.

Pertanyaan

lim _(x arrow 3) f(x)=(x^3-3 x^2-2 x+6)/(x-3)

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