# Step-by-step Solution

## Evaluate the limit of $\left(\frac{x+8x^2}{2x^2-1}\right)^{\frac{1}{2}}$ as $x$ approaches $\infty$

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### Videos

$\infty$

## Step-by-step explanation

Problem to solve:

$\lim_{x\to∞}\left(\frac{x+8x^2}{2x^2-1}\right)^{\frac{1}{2}}$
1

Evaluate the limit by replacing all occurrences of $x$ by $\infty$

$\sqrt{\frac{\infty +8\cdot \infty ^2}{2\cdot \infty ^2-1}}$
2

Simplifying

$\infty$

$\infty$

### Problem Analysis

$\lim_{x\to∞}\left(\frac{x+8x^2}{2x^2-1}\right)^{\frac{1}{2}}$

### Main topic:

Limits to Infinity

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