Evaluate the following limit: `lim_(x->oo)(5x^3-6)/(9+4x^3 )\ `

Explanation

To evaluate the limit \( \lim_{x \to \infty} \frac{5x^3 - 6}{9 + 4x^3} \), we can follow these steps:

### Step 1: Identify the highest power of \( x \)
In both the numerator and the denominator, the highest power of \( x \) is \( x^3 \).

### Step 2: Factor out \( x^3 \) from both the numerator and the denominator
We can rewrite the expression by factoring \( x^3 \) out of both the numerator and the denominator:

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