Express the following statement using Θ-notation: $$\left| x ^ { 5 } \right| \leq \left| \frac { 12 x ^ { 5 } ( 3 x + 4 ) } { x + 2 } \right| \leq 36 \left| x ^ { 5 } \right| \quad \text { for all real numbers } x 2$$

Name: Express the following statement using Θ-notation: \[\left| x ^ { 5 } \right| \leq \left| \frac { 12 x ^ { 5 } ( 3 x + 4 ) } { x + 2 } \right| \leq 36 \left| x ^ { 5 } \right| \quad \text { for all real numbers } x > 2\]
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Question

Express the following statement using Θ-notation: $$\left| x ^ { 5 } \right| \leq \left| \frac { 12 x ^ { 5 } ( 3 x + 4 ) } { x + 2 } \right| \leq 36 \left| x ^ { 5 } \right| \quad \text { for all real numbers } x > 2$$

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The Answer is

\frac { 12 x ^ { 5 } ( 3 x + 4 ) } { x + 2 } ext { is } \Theta \left( x ^ { 5 } ight)

Express the Following Statement Using Θ-Notation