Math Problem Statement

lim ​

x 4 +6x 5 −3x 2 +4 (2x 2 −3)(2x 3 −x) ​

Solution

It looks like you're trying to compute the limit of the following function:

lim⁡x→∞x4+6x5−3x2+4(2x2−3)(2x3−x)\lim_{x \to \infty} \frac{x^4 + 6x^5 - 3x^2 + 4}{(2x^2 - 3)(2x^3 - x)}

Let's break it down step by step:

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Math Problem Analysis

Mathematical Concepts

Calculus
Limits
Polynomials
Asymptotic Behavior

Formulas

Limit at infinity: lim_{x→∞} f(x)
Polynomial Division
Leading Term Approximation

Theorems

Limit Laws
Asymptotic Dominance of Polynomials

Suitable Grade Level

Grades 11-12 (Advanced Calculus)

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