Answered: 2-x+x* lim * 5x* – 3x

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter4: Polynomials

Section4.6: Multiplying Polynomials

Problem 48WE

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Explanation:

Given that,

$\underset{x \to \infty}{l i m} \frac{2 - x + x^{4}}{5 x^{4} - 3 x^{2}}$

If we directly put the x limit, we get $\frac{\infty}{\infty}$

We will take x⁴ common from top and bottom.

$\underset{x \to \infty}{l i m} \frac{x^{4} (\frac{2}{x^{4}} - \frac{x}{x^{4}} + \frac{x^{4}}{x^{4}})}{x^{4} (\frac{5 x^{4}}{x^{4}} - \frac{3 x^{2}}{x^{4}})} \underset{x \to \infty}{l i m} \frac{(\frac{2}{x^{4}} - \frac{1}{x^{3}} + 1)}{(5 - \frac{3}{x^{2}})}$

Now find the limit

$\frac{1}{\infty}$ is same as 0

$= \frac{0 - 0 + 1}{5 - 0} = \frac{1}{5}$

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