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Consider a system governed by the following equations:
$$\frac{{{\text{d}}{{\text{x}}_1}\left( {\text{t}} \right)}}{{{\text{dt}}}} = {{\text{x}}_2}\left( {\text{t}} \right) - {{\text{x}}_1}\left( {\text{t}} \right);\,\frac{{{\text{d}}{{\text{x}}_2}\left( {\text{t}} \right)}}{{{\text{dt}}}} = {{\text{x}}_1}\left( {\text{t}} \right) - {{\text{x}}_2}\left( {\text{t}} \right)$$
The initial conditions are such that $${{\text{x}}_1}\left( 0 \right) < {{\text{x}}_2}\left( 0 \right) < \infty .$$ Let $${{\text{x}}_{1{\text{f}}}} = \mathop {\lim }\limits_{{\text{t}} \to \infty } {{\text{x}}_1}\left( {\text{t}} \right)$$ and $${{\text{x}}_{2{\text{f}}}} = \mathop {\lim }\limits_{{\text{t}} \to \infty } {{\text{x}}_2}\left( {\text{t}} \right).$$ Which one of the following is true?

A. $${{\text{x}}_{1{\text{f}}}} < {{\text{x}}_{2{\text{f}}}} < \infty $$

B. $${{\text{x}}_{2{\text{f}}}} < {{\text{x}}_{1{\text{f}}}} < \infty $$

C. $${{\text{x}}_{1{\text{f}}}} = {{\text{x}}_{2{\text{f}}}} < \infty $$

D. $${{\text{x}}_{1{\text{f}}}} = {{\text{x}}_{2{\text{f}}}} = \infty $$

Answer: Option C

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Consider a system governed by the following equations frac text d...

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