Answered: x + 2x? + x lim .4 + x* + 2x + 2

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

Section4.3: Multiplying Monomials

Problem 42WE

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Use properties of limits to find the indicated limit (as shown). It may be necessary to rewrite an expression before limit properties can be applied.

Expert Solution

Step 1

Consider the following limit:

$\begin{array}{rcl} \lim_{x \to - 1} \frac{x^{3} + 2 x^{2} + x}{x^{4} + x^{3} + 2 x + 2} & = & \lim_{x \to - 1} \frac{x (x^{2} + 2 x + 1)}{x^{3} (x + 1) + 2 (x + 1)} \\ = & \lim_{x \to - 1} \frac{x {(x + 1)}^{2}}{(x^{3} + 2) (x + 1)} \\ = & \lim_{x \to - 1} \frac{x (x + 1)}{x^{3} + 2} \\ = & \frac{(- 1) (- 1 + 1)}{{(- 1)}^{3} + 2} \\ = & 0 \end{array}$

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