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

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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 and see if we can directly substitute \( x = -3 \). If we substitute \( x = -3 \) directly into the function, we get:

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

Simplifying the numerator:

\[
(-3)^3 = -27
\]
\[
-3(-3)^2 = -3(9) = -27
\]
\[
-2(-3) = 6
\]
\[
6 = 6
\]

So the numerator becomes:

\[
-27 - 27 + 6 + 6 = -42
\]

And the denominator is:

\[
-3 - 3 = -6
\]

Thus, we have:

\[
f(-3) = \frac{-42}{-6} = 7
\]

Since we were able to substitute \( x = -3 \) directly and the expression is defined, the limit is:

\[
\lim_{x \rightarrow -3} f(x) = 7
\]

Pertanyaan

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

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