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The given problem asks for the limit of a complex expression. Here's the breakdown:

We are given the condition:

\[
\lim_{x \to 2} \left( \sqrt[3]{\frac{a}{x^3} + \frac{b}{x^3} - 1} \right) = A
\]

Now, we are asked to find:

\[
\lim_{x \to 2} \left( \sqrt[3]{\frac{a}{27} + \frac{b}{27x^3} + x - 1} \right)
\]

### Step 1: Calculate the first limit
For the first limit, we need to analyze the expression when \( x \to 2 \). Substituting \( x = 2 \):

\[
\lim_{x \to 2} \left( \sqrt[3]{\frac{a}{x^3} + \frac{b}{x^3} - 1} \right)
\]

At \( x = 2 \), we get:

\[
\frac{a}{2^3} + \frac{b}{2^3} - 1 = \frac{a}{8} + \frac{b}{8} - 1 = \frac{a + b}{8} - 1
\]

This equals \( A \), so:

\[
A = \frac{a + b}{8} - 1 \quad \Rightarrow \quad A = \frac{a + b - 8}{8}
\]

### Step 2: Calculate the second limit
Now, for the second expression, substitute \( x = 2 \) into:

\[
\lim_{x \to 2} \left( \sqrt[3]{\frac{a}{27} + \frac{b}{27x^3} + x - 1} \right)
\]

Substituting \( x = 2 \):

\[
\frac{a}{27} + \frac{b}{27(2^3)} + 2 - 1 = \frac{a}{27} + \frac{b}{27 \times 8} + 1 = \frac{a}{27} + \frac{b}{216} + 1
\

Jika lim(x→2) (∛(a/x³ + b/x³ - 1)) = A, maka nilai lim(x→2) (∛(a/27 + b/27x³ + x - 1)) adalah?

Solve the limit of a cubic root expression involving algebraic terms. Learn the step-by-step process for substituting values and simplifying complex limits with cubic roots. Suitable for high school students in grades 11-12.

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